Simplify 2 natural log of x^3-3 natural log of x

$2 \ln (x^{3}) - 3 \ln (x)$

Step 1

Simplify each term.

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

$\ln ({(x^{3})}^{2}) - 3 \ln (x)$

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

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

$\ln (x^{3 \cdot 2}) - 3 \ln (x)$

Multiply $3$ by $2$ .

$\ln (x^{6}) - 3 \ln (x)$

Simplify $- 3 \ln (x)$ by moving $3$ inside the logarithm.

$\ln (x^{6}) - \ln (x^{3})$

Step 2

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

$\ln (\frac{x^{6}}{x^{3}})$

Step 3

Cancel the common factor of $x^{6}$ and $x^{3}$ .

Factor $x^{3}$ out of $x^{6}$ .

$\ln (\frac{x^{3} x^{3}}{x^{3}})$

Cancel the common factors.

Multiply by $1$ .

$\ln (\frac{x^{3} x^{3}}{x^{3} \cdot 1})$

Cancel the common factor.

$\ln (\frac{x^{3} x^{3}}{x^{3} \cdot 1})$

Rewrite the expression.

$\ln (\frac{x^{3}}{1})$

Divide $x^{3}$ by $1$ .

$\ln (x^{3})$