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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
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Tutti i libri di testoBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblema 21
Capitolo 5, Problema 21

Evaluate each expression without using a calculator. log4 16

Guida verificata passo dopo passo
1
Recognize that the expression \( \log_4 16 \) asks for the exponent to which the base 4 must be raised to get 16.
Express 16 as a power of 4. Since 16 is \( 4^2 \), rewrite the expression as \( \log_4 (4^2) \).
Use the logarithmic identity \( \log_b (b^k) = k \) to simplify \( \log_4 (4^2) \) to 2.
Conclude that \( \log_4 16 = 2 \) because 4 raised to the power 2 equals 16.
Thus, the value of the logarithm is the exponent 2.

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Logarithm Definition

A logarithm answers the question: to what exponent must the base be raised to produce a given number? For example, log_b(a) = c means b^c = a. Understanding this definition is essential to evaluate logarithmic expressions.
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Logarithms Introduction

Properties of Exponents

Since logarithms are closely related to exponents, knowing how to express numbers as powers of a base helps simplify logarithms. For instance, recognizing that 16 = 4^2 allows you to rewrite log_4(16) as log_4(4^2).
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Rational Exponents

Logarithm Power Rule

The power rule states that log_b(a^n) = n * log_b(a). This property allows you to bring the exponent in the argument down as a multiplier, simplifying the evaluation of logarithms when the argument is a power of the base.
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Power Rules
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