Answer
a.) x = 64
b.) x = -2
Work Step by Step
$Use$ $the$ $definition$ $of$ $the$ $logarithmic$ $function$ $to$ $find$ $x:$
a.) $\log_4 x = 3$
b.) $\log_{10} 0.01 = x$
a.) $\log_4 x = 3$
Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
$\log_4 x = 3 \rightarrow 4^3 = x$
$x = 4^3$
$x = 64$
b.) $\log_{10} 0.01 = x$
Rewrite the logarithmic form to exponential form: $\log_b a = c \rightarrow b^c = a$
$\log_{10} 0.01 = x \rightarrow 10^x = 0.01$
[When turning 0.01 into a fraction, we get $\frac{1}{100}$, which happens to expand to be $\frac{1}{10\times10}$. We can convert it then to $10^{-2}$]
$10^x = 10^{-2}$
$x = -2$