Precalculus Examples

$\frac{\frac{\log (\frac{12}{10})}{\log (1.01)} - 1}{2}$

Step 1

Cancel the common factor of $12$ and $10$ .

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Step 1.1

Factor $2$ out of $12$ .

$\frac{\frac{\log (\frac{2 (6)}{10})}{\log (1.01)} - 1}{2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $10$ .

$\frac{\frac{\log (\frac{2 \cdot 6}{2 \cdot 5})}{\log (1.01)} - 1}{2}$

Step 1.2.2

Cancel the common factor.

$\frac{\frac{\log (\frac{2 \cdot 6}{2 \cdot 5})}{\log (1.01)} - 1}{2}$

Step 1.2.3

Rewrite the expression.

$\frac{\frac{\log (\frac{6}{5})}{\log (1.01)} - 1}{2}$

Step 2

Log base $10$ of $1.01$ is approximately $0.00432137$ .

$\frac{\frac{\log (\frac{6}{5})}{0.00432137} - 1}{2}$

Step 3

Simplify the numerator.

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Step 3.1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{0.00432137}{0.00432137}$ .

$\frac{\frac{\log (\frac{6}{5})}{0.00432137} - 1 \cdot \frac{0.00432137}{0.00432137}}{2}$

Step 3.2

Combine $- 1$ and $\frac{0.00432137}{0.00432137}$ .

$\frac{\frac{\log (\frac{6}{5})}{0.00432137} + \frac{- 1 \cdot 0.00432137}{0.00432137}}{2}$

Step 3.3

Combine the numerators over the common denominator.

$\frac{\frac{\log (\frac{6}{5}) - 1 \cdot 0.00432137}{0.00432137}}{2}$

Step 3.4

Multiply $- 1$ by $0.00432137$ .

$\frac{\frac{\log (\frac{6}{5}) - 0.00432137}{0.00432137}}{2}$

Step 3.5

Divide $6$ by $5$ .

$\frac{\frac{\log (1.2) - 0.00432137}{0.00432137}}{2}$

Step 3.6

Log base $10$ of $1.2$ is approximately $0.07918124$ .

$\frac{\frac{0.07918124 - 0.00432137}{0.00432137}}{2}$

Step 3.7

Subtract $0.00432137$ from $0.07918124$ .

$\frac{\frac{0.07485987}{0.00432137}}{2}$

Step 3.8

Divide $0.07485987$ by $0.00432137$ .

$\frac{17.32316527}{2}$

Step 4

Divide $17.32316527$ by $2$ .

$8.66158263$