Answer
False,
$\displaystyle \log(\frac{x+2}{x-1}) = \log(x+2)-\log(x-1)$
Work Step by Step
The LHS is a quotient OF logarithms. No rule/property exists with which we can expand or simplify.
The RHS is a diffeence of logarithms, which appears in
the Quotient Rule (on its RHS):
$\displaystyle \log_{\mathrm{b}}(\frac{\mathrm{M}}{\mathrm{N}})=\log_{\mathrm{b}}\mathrm{M}-\log_{\mathrm{b}}\mathrm{N}$,
so
statement RHS = $\displaystyle \log(x+2)-\log(x-1)=\log(\frac{x+2}{x-1}),$
which does not equal the LHS of the problem statement.
So, the statement is false.
To make it true, change the LHS to $\displaystyle \log(\frac{x+2}{x-1})$
