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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
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Ch. 4 - Exponential and Logarithmic Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- 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
Capitolo 5, Problema 17
Write each equation in its equivalent logarithmic form. b3 = 1000
Guida verificata passo dopo passo1
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.
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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.
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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.
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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.
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04:06Rational Exponents
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