Domanda del libro di testo
In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4-1.5
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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 5
Write each equation in its equivalent exponential form. 5= logb 32
Guida verificata passo dopo passo1
Recall the definition of logarithm: if \(y = \log_b x\), then the equivalent exponential form is \(b^y = x\).
Identify the parts of the given equation \(5 = \log_b 32\): here, \(y = 5\), \(b\) is the base, and \(x = 32\).
Apply the definition by rewriting the logarithmic equation \(5 = \log_b 32\) as an exponential equation: \(b^5 = 32\).
This expresses the original logarithmic statement in exponential form, showing the relationship between the base \(b\), the exponent \(5\), and the result \(32\).
No further simplification is needed unless you are asked to solve for \(b\) or another variable.
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Definition of Logarithms
A logarithm answers the question: to what exponent must the base be raised to produce a given number? In the expression log_b(a) = c, b is the base, a is the result, and c is the exponent such that b^c = a.
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7:30
Logarithms Introduction
Converting Logarithmic to Exponential Form
To rewrite a logarithmic equation log_b(a) = c in exponential form, express it as b^c = a. This conversion is fundamental for solving equations involving logarithms by switching between forms.
Video consigliato:
04:34Converting Standard Form to Vertex Form
Properties of Exponents
Understanding how exponents work, such as the meaning of b^c and how to manipulate exponential expressions, is essential when converting between logarithmic and exponential forms and solving related equations.
Video consigliato:
04:06Rational Exponents
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