Let $f (x) = \log_{x^2} 25$ and $g(x) = \log_x 5$. Then, $f(x) = g(x)$ holds for x belonging to

$\{x:0 < x < ∞, x≠1\}$

We have,

$f (x) = \log_{x^2} 25=f (x) = \log_{x^2} 5^2=\frac{5}{2} \log_x5=\log_x5=g(x)$

for all x in their common domain.

Now, $D_1$ =Domain of f = $R^+ - \{0,-1,1\}$

and, $D_2$ = Domain of g = ${x: x > 0, x ≠ 1}$

$∴D_1 ∩D_2 = \{x:x > 0, x ≠ 1\}$.

Thus, $f (x) = g(x)$ for all $x ∈ \{x: x > 0, x ≠ 1\}$.