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

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

Simplify each term.

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

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

Simplify $3 \log (x^{2})$ by moving $3$ inside the logarithm.

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

Multiply the exponents in ${(x^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $2$ by $3$ .

$\log (x^{5}) + \log (x^{6})$

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

$\log (x^{5} x^{6})$

Multiply $x^{5}$ by $x^{6}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\log (x^{5 + 6})$

Add $5$ and $6$ .

$\log (x^{11})$