Simplify log base 7 of x^3- log base 7 of x

$\log_{7} (x^{3}) - \log_{7} (x)$

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

$\log_{7} (\frac{x^{3}}{x})$

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

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

$\log_{7} (\frac{x \cdot x^{2}}{x})$

Cancel the common factors.

Raise $x$ to the power of $1$ .

$\log_{7} (\frac{x \cdot x^{2}}{x^{1}})$

Factor $x$ out of $x^{1}$ .

$\log_{7} (\frac{x \cdot x^{2}}{x \cdot 1})$

Cancel the common factor.

$\log_{7} (\frac{x \cdot x^{2}}{x \cdot 1})$

Rewrite the expression.

$\log_{7} (\frac{x^{2}}{1})$

Divide $x^{2}$ by $1$ .

$\log_{7} (x^{2})$