Write as a Single Logarithm 5 log base 7 of x-2 log base 7 of x

$5 \log_{7} (x) - 2 \log_{7} (x)$

Step 1

Simplify each term.

Simplify $5 \log_{7} (x)$ by moving $5$ inside the logarithm.

$\log_{7} (x^{5}) - 2 \log_{7} (x)$

Simplify $- 2 \log_{7} (x)$ by moving $2$ inside the logarithm.

$\log_{7} (x^{5}) - \log_{7} (x^{2})$

Step 2

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

$\log_{7} (\frac{x^{5}}{x^{2}})$

Step 3

Cancel the common factor of $x^{5}$ and $x^{2}$ .

Factor $x^{2}$ out of $x^{5}$ .

$\log_{7} (\frac{x^{2} x^{3}}{x^{2}})$

Cancel the common factors.

Multiply by $1$ .

$\log_{7} (\frac{x^{2} x^{3}}{x^{2} \cdot 1})$

Cancel the common factor.

$\log_{7} (\frac{x^{2} x^{3}}{x^{2} \cdot 1})$

Rewrite the expression.

$\log_{7} (\frac{x^{3}}{1})$

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

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