Answer
$\text{false}$
Work Step by Step
Note that
$$\dfrac{\ln 8}{\ln 4}=\dfrac{\ln 2^{3}}{\ln 2^{2}}$$
Using the rule $\ln a^{m}=m \ln a$ yields
$$\require{cancel}\dfrac{\ln 8}{\ln 4}=\dfrac{3 \ln 2}{2 \ln 2}=\dfrac{3 \cancel{\ln 2}}{2 \cancel{\ln 2}}=\dfrac{3}{2}$$
Therefore
$$\dfrac{\ln 8}{\ln 4}=\frac{3}{2}\ne2$$
The given statement is false.
