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

$\{x:0 < x < ∞, x≠1\}$

The correct answer is Option (2) → $\{x:0 < x < ∞, x≠1\}$

We have,

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

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 $x ∈ \{x: x > 0, x≠ 1\}$