Simplify/Condense 5 log of x-2 log of 4

$5 \log (x) - 2 \log (4)$

Step 1

Simplify each term.

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

$\log (x^{5}) - 2 \log (4)$

Simplify $- 2 \log (4)$ by moving $2$ inside the logarithm.

$\log (x^{5}) - \log (4^{2})$

Raise $4$ to the power of $2$ .

$\log (x^{5}) - \log (16)$

Step 2

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\log (\frac{x^{5}}{16})$