Textbook Question
Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2x=64
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Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Chapter 5, Problem 1
Write each equation in its equivalent exponential form. 4 = log2 16
Verified step by step guidance1
Recall the definition of logarithm: if \(y = \log_{b} x\), then the equivalent exponential form is \(b^{y} = x\).
Identify the base \(b\), the exponent \(y\), and the result \(x\) from the given equation \(4 = \log_{2} 16\).
Here, the base \(b\) is 2, the exponent \(y\) is 4, and the result \(x\) is 16.
Apply the definition by rewriting the logarithmic equation as an exponential equation: \(2^{4} = 16\).
This shows the equivalent exponential form of the given logarithmic equation.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Definition of Logarithms
A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log₂ 16 means the exponent to which 2 must be raised to get 16.
Recommended video:
7:30
Logarithms Introduction
Conversion Between Logarithmic and Exponential Forms
Logarithmic and exponential forms are two ways to express the same relationship. The equation log_b a = c is equivalent to the exponential form b^c = a, where b is the base, c is the exponent, and a is the result.
Recommended video:
5:02Solving Logarithmic Equations
Properties of Exponents
Understanding how exponents work helps verify conversions. For example, knowing that 2^4 = 16 confirms that log₂ 16 = 4, reinforcing the connection between logarithms and exponents.
Recommended video:
04:06Rational Exponents
Related Practice
Textbook Question
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
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 1–10, approximate each number using a calculator. Round your answer to three decimal places. 23.4
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Textbook Question
The graph of an exponential function is given. Select the function for each graph from the following options: f(x) = 4x, g(x) = 4-x, h(x) = -4-x, r(x) = -4-x+3
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