Precalculus Examples

$\log_{6} (\frac{x^{2} - 9}{25 x^{2}})$

Step 1

Rewrite $\log_{6} (\frac{x^{2} - 9}{25 x^{2}})$ as $\log_{6} (x^{2} - 9) - \log_{6} (25 x^{2})$ .

$\log_{6} (x^{2} - 9) - \log_{6} (25 x^{2})$

Step 2

Rewrite $\log_{6} (25 x^{2})$ as $\log_{6} (25) + \log_{6} (x^{2})$ .

$\log_{6} (x^{2} - 9) - (\log_{6} (25) + \log_{6} (x^{2}))$

Step 3

Expand $\log_{6} (x^{2})$ by moving $2$ outside the logarithm.

$\log_{6} (x^{2} - 9) - (\log_{6} (25) + 2 \log_{6} (x))$

Step 4

Simplify each term.

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Step 4.1

Simplify each term.

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Step 4.1.1

Rewrite $\log_{6} (25)$ as $\log_{6} (5^{2})$ .

$\log_{6} (x^{2} - 9) - (\log_{6} (5^{2}) + 2 \log_{6} (x))$

Step 4.1.2

Expand $\log_{6} (5^{2})$ by moving $2$ outside the logarithm.

$\log_{6} (x^{2} - 9) - (2 \log_{6} (5) + 2 \log_{6} (x))$

Step 4.2

Apply the distributive property.

$\log_{6} (x^{2} - 9) - (2 \log_{6} (5)) - (2 \log_{6} (x))$

Step 4.3

Multiply $2$ by $- 1$ .

$\log_{6} (x^{2} - 9) - 2 \log_{6} (5) - (2 \log_{6} (x))$

Step 4.4

Multiply $2$ by $- 1$ .

$\log_{6} (x^{2} - 9) - 2 \log_{6} (5) - 2 \log_{6} (x)$