## Intermediate Algebra for College Students (7th Edition)

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