Skip to main content
Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblem 17
Chapter 5, Problem 17

Write each equation in its equivalent logarithmic form. b3 = 1000

Verified step by step guidance
1
Identify the components of the exponential equation \(b^3 = 1000\). Here, \(b\) is the base, \(3\) is the exponent, and \(1000\) is the result.
Recall the definition of logarithms: If \(a^x = y\), then the equivalent logarithmic form is \(\log_a y = x\).
Apply this definition to the given equation by setting the base \(a\) as \(b\), the result \(y\) as \(1000\), and the exponent \(x\) as \(3\).
Write the logarithmic form as \(\log_b 1000 = 3\).
This expresses the original exponential equation in its equivalent logarithmic form.

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 and Logarithmic Forms

Exponential and logarithmic forms are two ways to express the same relationship. An equation like b^3 = 1000 can be rewritten in logarithmic form as log base b of 1000 equals 3. This conversion helps solve for unknown exponents or bases.
Recommended video:
5:02
Solving Logarithmic Equations

Definition of a Logarithm

A logarithm answers the question: to what power must the base be raised to get a certain number? Formally, if b^x = y, then log base b of y equals x. Understanding this definition is essential for rewriting exponential equations as logarithms.
Recommended video:
7:30
Logarithms Introduction

Properties of Exponents

Properties of exponents, such as b^m * b^n = b^(m+n), help manipulate and simplify exponential expressions. Recognizing these properties aids in understanding the structure of the equation before converting it to logarithmic form.
Recommended video:
Guided course
04:06
Rational Exponents
Related Practice
Textbook Question

Graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. f(x) = (0.6)x

944
views
Textbook Question

In Exercises 19–24, the graph of an exponential function is given. Select the function for each graph from the following options:

f(x)=3x,g(x)=3x−1,h(x)=3x−1,f(x)=−3x,G(x)=3−x,H(x)=−3−x.f(x) = 3^x, \(\quad\) g(x) = 3^{x-1}, \(\quad\) h(x) = 3^x - 1, \(\f\)(x) = -3^x, \(\quad\) G(x) = 3^{-x}, \(\quad\) H(x) = -3^{-x}.

1688
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. log N-6

893
views
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. 4x=1/√2

776
views
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. 8(x+3)=16(x−1)

970
views
Textbook Question

In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874

896
views