Precalculus Examples

$2 \log_{8} (9 x) - \log_{8} (2 x - 5)$

Step 1

Simplify each term.

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Step 1.1

Simplify $2 \log_{8} (9 x)$ by moving $2$ inside the logarithm.

$\log_{8} ({(9 x)}^{2}) - \log_{8} (2 x - 5)$

Step 1.2

Apply the product rule to $9 x$ .

$\log_{8} (9^{2} x^{2}) - \log_{8} (2 x - 5)$

Step 1.3

Raise $9$ to the power of $2$ .

$\log_{8} (81 x^{2}) - \log_{8} (2 x - 5)$

Step 2

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

$\log_{8} (\frac{81 x^{2}}{2 x - 5})$