Precalculus Examples

$\log_{x} (\frac{25}{9})$

Step 1

Rewrite $\log_{x} (\frac{25}{9})$ as $\log_{x} (25) - \log_{x} (9)$ .

$\log_{x} (25) - \log_{x} (9)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log_{x} (25)$ as $\log_{x} (5^{2})$ .

$\log_{x} (5^{2}) - \log_{x} (9)$

Step 2.2

Expand $\log_{x} (5^{2})$ by moving $2$ outside the logarithm.

$2 \log_{x} (5) - \log_{x} (9)$

Step 2.3

Rewrite $\log_{x} (9)$ as $\log_{x} (3^{2})$ .

$2 \log_{x} (5) - \log_{x} (3^{2})$

Step 2.4

Expand $\log_{x} (3^{2})$ by moving $2$ outside the logarithm.

$2 \log_{x} (5) - (2 \log_{x} (3))$

Step 2.5

Multiply $2$ by $- 1$ .

$2 \log_{x} (5) - 2 \log_{x} (3)$