Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.3 - Logarithmic Functions - Exercise Set: 33

Answer

$x = \frac{1}{2}$

Work Step by Step

Let $\log_{64}{8} = x$ RECALL: $\log_b{y} =x \longrightarrow b^x=y$ Use the rule above, where $y=8$ and $b=64$, to obtain: $64^x=8^{1}$ Write 64 as $8^2$ to obtain: $(8^2)^x=8^{1} \\8^{2x} = 8^{1}$ Use the rule "If $a^x=a^y$, then $x=y$" to obtain: $2x=1 \\x = \frac{1}{2}$
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