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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 81
Capitolo 5, Problema 81

Evaluate or simplify each expression without using a calculator. log 100

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Recall the definition of the logarithm: \(\log_b a = c\) means that \(b^c = a\). Here, the base is 10 since it is a common logarithm (log without a base is base 10).
Rewrite the expression \(\log 100\) as \(\log_{10} 100\) to emphasize the base 10.
Express 100 as a power of 10: \(100 = 10^2\).
Use the logarithm power rule: \(\log_b (a^c) = c \log_b a\). Applying this, \(\log_{10} (10^2) = 2 \log_{10} 10\).
Since \(\log_{10} 10 = 1\), simplify the expression to \(2 \times 1 = 2\).

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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 base 10 of 100 asks, '10 raised to what power equals 100?' Understanding this definition is fundamental to evaluating logarithmic expressions.
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Logarithms Introduction

Common Logarithms (Base 10)

Common logarithms use base 10 and are often written simply as log without a base. Since 100 = 10^2, log 100 means log base 10 of 100, which equals 2. Recognizing powers of 10 helps simplify these expressions quickly.
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Graphs of Common Functions

Properties of Logarithms

Logarithms have properties like log(a^b) = b * log(a), which allow simplification of expressions. Applying these properties helps evaluate or simplify logarithmic expressions without a calculator by rewriting numbers as powers of the base.
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Change of Base Property
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