Simplify/Condense 5 log base 7 of a-2 log base 7 of a

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

Simplify each term.

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

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

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

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

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

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

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

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

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

Cancel the common factors.

Multiply by $1$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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