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Ch. 4 - Exponential and Logarithmic Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 4 - Exponential and Logarithmic FunctionsProblema 37
Capitolo 5, Problema 37

Evaluate each expression without using a calculator. log4 1

Guida verificata passo dopo passo
1
Recall the definition of logarithm: \(\log_b a = c\) means that \(b^c = a\).
In this problem, we have \(\log_4 1\), so we want to find the exponent \(c\) such that \(4^c = 1\).
Remember that any nonzero number raised to the power of 0 equals 1, i.e., \(b^0 = 1\) for \(b \neq 0\).
Since \(4^0 = 1\), it follows that \(\log_4 1 = 0\).
Therefore, the value of \(\log_4 1\) is the exponent that makes the base 4 equal to 1, which is 0.

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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? 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

Logarithm of 1

For any positive base b (b ≠ 1), log_b(1) is always 0 because b raised to the power 0 equals 1. This property simplifies evaluating logarithms where the argument is 1.
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Logarithms Introduction

Properties of Logarithms Without a Calculator

Evaluating logarithms without a calculator relies on recognizing special values and applying logarithmic properties, such as log_b(b) = 1 and log_b(1) = 0. Familiarity with these properties allows quick simplification.
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Change of Base Property
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