Precalculus Examples

$\log_{w} (\frac{13 x}{4})$

Step 1

Rewrite $\log_{w} (\frac{13 x}{4})$ as $\log_{w} (13 x) - \log_{w} (4)$ .

$\log_{w} (13 x) - \log_{w} (4)$

Step 2

Rewrite $\log_{w} (13 x)$ as $\log_{w} (13) + \log_{w} (x)$ .

$\log_{w} (13) + \log_{w} (x) - \log_{w} (4)$

Step 3

Simplify each term.

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Step 3.1

Rewrite $\log_{w} (4)$ as $\log_{w} (2^{2})$ .

$\log_{w} (13) + \log_{w} (x) - \log_{w} (2^{2})$

Step 3.2

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

$\log_{w} (13) + \log_{w} (x) - (2 \log_{w} (2))$

Step 3.3

Multiply $2$ by $- 1$ .

$\log_{w} (13) + \log_{w} (x) - 2 \log_{w} (2)$