Precalculus Examples

$\frac{\log (\frac{15}{80})}{\log (0.965)}$

Step 1

Cancel the common factor of $15$ and $80$ .

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Step 1.1

Factor $5$ out of $15$ .

$\frac{\log (\frac{5 (3)}{80})}{\log (0.965)}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $80$ .

$\frac{\log (\frac{5 \cdot 3}{5 \cdot 16})}{\log (0.965)}$

Step 1.2.2

Cancel the common factor.

$\frac{\log (\frac{5 \cdot 3}{5 \cdot 16})}{\log (0.965)}$

Step 1.2.3

Rewrite the expression.

$\frac{\log (\frac{3}{16})}{\log (0.965)}$

Step 2

Log base $10$ of $0.965$ is approximately $- 0.01547268$ .

$\frac{\log (\frac{3}{16})}{- 0.01547268}$

Step 3

Move the negative in front of the fraction.

$- \frac{\log (\frac{3}{16})}{0.01547268}$

Step 4

Divide $3$ by $16$ .

$- \frac{\log (0.1875)}{0.01547268}$

Step 5

Log base $10$ of $0.1875$ is approximately $- 0.72699872$ .

$- \frac{- 0.72699872}{0.01547268}$

Step 6

Divide $- 0.72699872$ by $0.01547268$ .

$- - 46.98594006$

Step 7

Multiply $- 1$ by $- 46.98594006$ .

$46.98594006$