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Multiple Choice

Write the log expression as a single log.

$\log_2\frac{1}{9x}+2\log_23x$

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Multiple Choice

Write the log expression as a single log.

$\ln\frac{3x}{y}+2\ln2y-\ln4x$

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Multiple Choice

Write the single logarithm as a sum or difference of logs.

$\log_3\left(\frac{\sqrt{x}}{9y^2}\right)$

Write the single logarithm as a sum or difference of logs.

$\log_5\left(\frac{5\left(2x+3\right)^2}{x^3}\right)$

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Multiple Choice

Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.

$\log_317$

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Multiple Choice

Evaluate the given logarithm using the change of base formula and a calculator. Use the common log.

$\log_967$

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Multiple Choice

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.

$\log_841$

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Multiple Choice

Evaluate the given logarithm using the change of base formula and a calculator. Use the natural log.

$\log_23789$

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log5 (7 × 3)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log7 (7x)

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Textbook Question

In Exercises 1–8, write each equation in its equivalent exponential form. 5= logb 32

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(1000x)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(1000x)

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Textbook Question

Answer each of the following. Write log_3 12 in terms of natural logarithms using the change-of-base theorem.

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log7 (7/x)

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Textbook Question

Answer each of the following. Between what two consecutive integers must log_2 12 lie?

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log(x/100)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 10^12

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (64/y)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (64/y)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln(e^2/5)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 0.1

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Textbook Question

In Exercises 13–15, write each equation in its equivalent exponential form. log3 81 = y

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb x^3

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. . log 63

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Textbook Question

If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. log￬√3 81 = 8

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 0.0022

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log N^(-6)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log N^(-6)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln 5√x (fifth root of)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log(387 * 23)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb (x^2 y)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 518/342

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 387 + log 23

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (√x/64)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (√x/64)

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log3 27

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Textbook Question

Solve each equation. x = 3^log3 8

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log6 (36/(√(x+1))

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 518 - log 342

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb ((x^2 y)/z^2)

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Textbook Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). grapefruit, 6.3*10^-4

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log √(100x)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log √(100x)

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Textbook Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). limes, 1.6*10^-2

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Textbook Question

Use a calculator to find an approximation to four decimal places for each logarithm. ln 144,000

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log ∛(x/y)

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Textbook Question

For each substance, find the pH from the given hydronium ion concentration to the nearest tenth. See Example 2(a). crackers, 3.9*10^-9

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. logb ((√x y^3)/z^3)

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Textbook Question

Find the [H_3O^+] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. See Example 2(b). soda pop, 2.7

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Textbook Question

Use a calculator to find an approximation to four decimal places for each logarithm. log₂/₃ 5/8

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Textbook Question

In Exercises 21–42, evaluate each expression without using a calculator. log5 5

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Textbook Question

Solve each equation. log￬9 x = 5/2

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Textbook Question

Find the [H_3O^+] for each substance with the given pH. Write answers in scientific notation to the nearest tenth. See Example 2(b). beer, 4.8

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log5 ∛((x^2 y)/24)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log5 ∛((x^2 y)/24)

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Textbook Question

In Exercises 36–38, begin by graphing f(x) = log2 x Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. g(x) = log2 (x-2)

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln[(x^3(√(x^2 + 1))/(x + 1)^4]

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Textbook Question

Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-5

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Textbook Question

In Exercises 1–40, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log [(10x^2∛(1 - x))/(7(x + 1)^2)]

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Textbook Question

Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-2

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Textbook Question

Suppose that water from a wetland area is sampled and found to have the given hydronium ion concentration. Determine whether the wetland is a rich fen, a poor fen, or a bog. See Example 3. 2.49*10^-7

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log 5 + log 2

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log 5 + log 2

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Textbook Question

Solve each problem. Use a calculator to find an approximation for each logarithm. log 398.4

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. ln x + ln 7

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Textbook Question

Solve each problem. Use a calculator to find an approximation for each logarithm. log 3.984

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log2 (96) - log2 (3)

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln e^1.6

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 1/e^2

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log x + 3 log y

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. log x + 3 log y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln √e

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Textbook Question

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. log4 (√x/64)

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)ln x + ln y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 28

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 2 logb x + 3 logb y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 0.00013

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Textbook Question

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln ∛(x/e)

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Textbook Question

In Exercises 50–53, use properties of logarithms to expand each logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. ln ∛(x/e)

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Textbook Question

Graph each function. ƒ(x) = log￬3 (x-1) + 2

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Textbook Question

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. log 3 - 3 log x

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 5 ln x - 2 ln y

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 5 ln x - 2 ln y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln (27 * 943)

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Textbook Question

In Exercises 54–57, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. 1/2 ln x - ln y

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 3 ln x - (1/3) ln y

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 98/13

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 4 ln (x + 6) - 3 ln x

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 27 + ln 943

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Textbook Question

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log4 0.863

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Textbook Question

In Exercises 58–59, use common logarithms or natural logarithms and a calculator to evaluate to four decimal places. log4 0.863

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 3 ln x + 5 ln y - 6 ln z

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. 3 ln x + 5 ln y - 6 ln z

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 98 - ln 13

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Textbook Question

Find each value. If applicable, give an approximation to four decimal places. See Example 5. ln 84 - ln 17

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)(log x + log y)

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Textbook Question

Graph each function. Give the domain and range. ƒ(x) = | log￬1/2 (x-2) |

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Textbook Question

In Exercises 41–70, use properties of logarithms to condense each logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions without using a calculator. (1/2)(log5 x + log5 y) - 2 log5 (x + 1)

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Textbook Question

The figure shows the graph of f(x) = ln x. In Exercises 65–74, use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range.

h(x) = ln (2x)

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6. Exponential & Logarithmic Functions

Properties of Logarithms

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