Ch. 4 - Inverse, Exponential, and Logarithmic Functions
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- Fill in the blank(s) to correctly complete each sentence. If ƒ(x) = 4^x, then ƒ(2) = and ƒ(-2) = ________.
Problem 1
- Answer each of the following. Write log_3 12 in terms of natural logarithms using the change-of-base theorem.
Problem 6
- Solve each equation. Round answers to the nearest hundredth as needed. (1/4)^x=64
Problem 7
- Answer each of the following. Between what two consecutive integers must log_2 12 lie?
Problem 8
- Solve each equation. Round answers to the nearest hundredth as needed. x^(2/3) =36
Problem 8
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. 3^x = 7
Problem 11
- 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. 3^4 = 81
Problem 11
- Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 10^12
Problem 11
- For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(-2)
Problem 13
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. (1/2)^x = 5
Problem 13
- Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 0.1
Problem 13
- For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(2)
Problem 15
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. 0.8^x = 4
Problem 15
- Find each value. If applicable, give an approximation to four decimal places. See Example 1. . log 63
Problem 15
- 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￬5 5 = 1
Problem 16
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. 4^(x-1) = 3^2x
Problem 17
- 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
Problem 17
- Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 0.0022
Problem 17
- 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￬4 1/64 = -3
Problem 18
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. 6^(x+1) = 4^(2x-1)
Problem 19
- Find each value. If applicable, give an approximation to four decimal places. See Example 1. log(387 * 23)
Problem 19
- For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(-5/2)
Problem 20
- Solve each equation. x = log￬3 1/81
Problem 20
- For ƒ(x) = 3^x and g(x)= (1/4)^x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. g(3/2)
Problem 21
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. e^(x^2) = 100
Problem 21
- Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 518/342
Problem 21
- Solve each equation. log￬x 27/64 = 3
Problem 22
- Solve each equation. In Exercises 11–34, give irrational solutions as decimals correct to the nearest thousandth. In Exercises 35-40, give solutions in exact form. See Examples 1–4. e^(3x-7) • e^-2x = 4e
Problem 23
- Solve each equation. x = log￬8 ∜8
Problem 23
- Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 387 + log 23
Problem 23
