Solve for x log of x=2 log of 5+3 log of 4

$\log (x) = 2 \log (5) + 3 \log (4)$

Simplify the right side.

Simplify $2 \log (5) + 3 \log (4)$ .

Simplify each term.

Simplify $2 \log (5)$ by moving $2$ inside the logarithm.

$\log (x) = \log (5^{2}) + 3 \log (4)$

Raise $5$ to the power of $2$ .

$\log (x) = \log (25) + 3 \log (4)$

Simplify $3 \log (4)$ by moving $3$ inside the logarithm.

$\log (x) = \log (25) + \log (4^{3})$

Raise $4$ to the power of $3$ .

$\log (x) = \log (25) + \log (64)$

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

$\log (x) = \log (25 \cdot 64)$

Multiply $25$ by $64$ .

$\log (x) = \log (1600)$

For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.

$x = 1600$