Textbook Question
Solve each equation. Round answers to the nearest hundredth as needed. x^(2/3) =36
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Ch. 4 - Inverse, Exponential, and Logarithmic Functions
Chapter 5, Problem 11
Find each value. If applicable, give an approximation to four decimal places. See Example 1. log 10^12
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Logarithms
A logarithm is the power to which a base must be raised to produce a given number. In the expression log_b(a), 'b' is the base, 'a' is the number, and the result is the exponent 'x' such that b^x = a. Understanding logarithms is essential for solving equations involving exponential growth or decay.
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Logarithms Introduction
Properties of Logarithms
Logarithms have several key properties that simplify calculations, such as the product, quotient, and power rules. For example, log_b(mn) = log_b(m) + log_b(n) and log_b(m/n) = log_b(m) - log_b(n). These properties allow for the manipulation of logarithmic expressions to solve complex problems.
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5:36Change of Base Property
Common Logarithm
The common logarithm is a logarithm with base 10, denoted as log(x) or log_10(x). It is widely used in scientific calculations and can be easily computed using calculators. For instance, log(10^12) simplifies to 12, as 10 raised to the power of 12 equals 10^12.
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Related Practice
Textbook Question
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
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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. 3^4 = 81
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Textbook Question
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)
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Textbook Question
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
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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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