College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises: 35

Answer

(a) $x=64$ (b) $x=-2$

Work Step by Step

RECALL: $\log_b{x}=y \longrightarrow b^x=y$ Use the rule above to obtain: (a) $\begin{array}{ccc} &4^3&=&x \\&4(4)(4)&=&x \\&64&=&x \end{array}$ (b) $\begin{array}{ccc} &10^x&=&0.01 \\&10^x&=&\frac{1}{100} \\&10^x&=&\frac{1}{10^2} \end{array}$ Note that $\frac{1}{10^2} = 10^{-2}$. Thus, $\begin{array}{ccc} &10^x&=&10^{-2} \end{array}$ Use the rule $a^m=a^n \longrightarrow m=n$ to obtain: $x=-2$
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