Precalculus Examples

$\log (\frac{14}{3^{x}})$

Step 1

Rewrite $\log (\frac{14}{3^{x}})$ as $\log (14) - \log (3^{x})$ .

$\log (14) - \log (3^{x})$

Step 2

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

$\log (14) - (x \log (3))$

Step 3

Remove parentheses.

$\log (14) - x \log (3)$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log (14)$ as $\log (2 (7))$ .

$\log (2 (7)) - x \log (3)$

Step 4.2

Rewrite $\log (2 (7))$ as $\log (2) + \log (7)$ .

$\log (2) + \log (7) - x \log (3)$