Simplify/Condense 2 log base 5 of x+ log base 5 of 3

$2 \log_{5} (x) + \log_{5} (3)$

Simplify $2 \log_{5} (x)$ by moving $2$ inside the logarithm.

$\log_{5} (x^{2}) + \log_{5} (3)$

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\log_{5} (x^{2} \cdot 3)$

Move $3$ to the left of $x^{2}$ .

$\log_{5} (3 x^{2})$