Precalculus Examples

$\log_{9} (7^{5} \cdot 10^{2})$

Step 1

Rewrite $\log_{9} (7^{5} \cdot 10^{2})$ as $\log_{9} (7^{5}) + \log_{9} (10^{2})$ .

$\log_{9} (7^{5}) + \log_{9} (10^{2})$

Step 2

Expand $\log_{9} (7^{5})$ by moving $5$ outside the logarithm.

$5 \log_{9} (7) + \log_{9} (10^{2})$

Step 3

Expand $\log_{9} (10^{2})$ by moving $2$ outside the logarithm.

$5 \log_{9} (7) + 2 \log_{9} (10)$

Step 4

Rewrite $\log_{9} (10)$ as $\log_{9} (2 (5))$ .

$5 \log_{9} (7) + 2 \log_{9} (2 (5))$

Step 5

Rewrite $\log_{9} (2 (5))$ as $\log_{9} (2) + \log_{9} (5)$ .

$5 \log_{9} (7) + 2 (\log_{9} (2) + \log_{9} (5))$

Step 6

Apply the distributive property.

$5 \log_{9} (7) + 2 \log_{9} (2) + 2 \log_{9} (5)$