Skip to main content
Ch. 4 - Inverse, Exponential, and Logarithmic Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 4 - Inverse, Exponential, and Logarithmic FunctionsProblem 11
Chapter 5, 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. 34 = 81

Verified step by step guidance
1
Identify the components of the exponential equation \(3^4 = 81\). Here, the base is 3, the exponent (or power) is 4, and the result is 81.
Recall the relationship between exponential and logarithmic forms: an exponential equation \(a^b = c\) can be rewritten as a logarithmic equation \(\log_a c = b\), where \(a\) is the base, \(b\) is the exponent, and \(c\) is the result.
Apply this relationship to the given equation by setting the base of the logarithm to 3, the argument to 81, and the result to 4.
Write the equivalent logarithmic form as \(\log_3 81 = 4\).
This expresses the original exponential statement in logarithmic form, showing that the logarithm base 3 of 81 equals 4.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1m
Was this helpful?

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 an exponent, such as a^b = c, where 'a' is the base, 'b' is the exponent, and 'c' is the result. It shows repeated multiplication of the base.
Recommended video:
6:13
Exponential Functions

Logarithmic Form

Logarithmic form is the inverse of exponential form and is written as log_base(result) = exponent. It answers the question: 'To what power must the base be raised to get the result?'
Recommended video:
7:30
Logarithms Introduction

Conversion Between Exponential and Logarithmic Forms

Converting between forms involves rewriting a^b = c as log_a(c) = b, and vice versa. This conversion helps solve equations and understand relationships between exponents and logarithms.
Recommended video:
5:02
Solving Logarithmic Equations
Related Practice
Textbook Question

Solve each equation. Round answers to the nearest hundredth as needed. x2/3 =36

Textbook Question

For ƒ(x) = 3x and g(x)= (1/4)x find each of the following. Round answers to the nearest thousandth as needed. See Example 1. ƒ(2)

Textbook Question

Determine whether each function graphed or defined is one-to-one.

Textbook Question

For ƒ(x) = 3x and g(x)= (1/4)x find each of the following. Round answers to the nearest thousandth as needed. ƒ(-2)

Textbook Question

Find each value. If applicable, give an approximation to four decimal places. log 1012

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. 3x = 7