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
1
views
Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
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 17
Write each equation in its equivalent logarithmic form. b3 = 1000
Verified step by step guidance1
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:
1mWas 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:
7:30Logarithms 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
04:06Rational 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. log N-6
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
Textbook Question
Write each equation in its equivalent logarithmic form. 132 = x
Textbook Question
In Exercises 16–18, write each equation in its equivalent logarithmic form. 13^y = 874
2
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. 6(x−3)/4=√6