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. g(2)
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Ch. 4 - Inverse, Exponential, and Logarithmic Functions
Chapter 5, Problem 16
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
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Exponential Form
Exponential form expresses a number as a base raised to a power, typically written as b^y = x, where b is the base, y is the exponent, and x is the result. This form is fundamental in understanding how logarithms work, as logarithms are the inverse operations of exponentiation.
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Exponential Functions
Logarithmic Form
Logarithmic form represents the exponent to which a base must be raised to produce a given number, expressed as log_b(x) = y. In this equation, b is the base, x is the result, and y is the exponent. Understanding this relationship is crucial for converting between exponential and logarithmic forms.
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7:30Logarithms Introduction
Inverse Relationships
The relationship between exponential and logarithmic forms is one of inverse operations. This means that if you have an equation in exponential form, you can convert it to logarithmic form and vice versa. Recognizing this inverse relationship is essential for solving problems that require switching between these two forms.
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4:30Graphing Logarithmic Functions
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.
0.8^x = 4
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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
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
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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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