Answer
False
Work Step by Step
We are given the following expression:
$(\log{x})^2\stackrel{?}{=}\log{x^2}$
Recall the power property of logarithms (pg. 462):
$\log_b{m^n}=n\log_b{m}$
We apply this property to the right side of our expression:
$(\log{x})^2\stackrel{?}{=}2\log{x}$
$\log{x}\times\log{x}\ne\log{x}+\log{x}$
We see that the statement mistakes addition for multiplication and is therefore false.
