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:
$x=-2$
