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
Ch. 4 - Exponential and Logarithmic Functions

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.

Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mWas this helpful?
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:
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:
Solving 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:
Guided course
Rational Exponents
Related Practice
Textbook Question
595
views
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)
928
views
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)
921
views
Textbook Question
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 23.4
871
views
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
1333
views
