Answer
Solution set = $\{28\}.$
Work Step by Step
For the equation to be defined, logarithms must have positive arguments
$ x \gt -1/7 \qquad (*)$
This is the condition eventual solutions must satisfy.
$ 2\log x-\log 7=\log 112\qquad $... LHS: power rule
$\log x^{2}-\log 7=\log 112 \qquad $... LHS: quotient rule
$\displaystyle \log\frac{x^{2}}{7}=\log \mathrm{l}12 \quad $ ... $\log $ is one-to-one
$\displaystyle \frac{x^{2}}{7}=112 \quad $ ... /$\times 7$
$ x^{2}=784$
$ x=\pm 28$
$ x=28 \qquad $ ... satisfies (*)
$ x=-28 \quad $ ... does not satisfy (*)
Thus, the solution set = $\{28\}.$
