Precalculus Examples

$\frac{0.01}{1 + 0.5} \cdot \frac{\log (8) \cdot 141.333}{100}$

Step 1

Cancel the common factor of $0.01$ .

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Step 1.1

Add $1$ and $0.5$ .

$\frac{0.01}{1.5} \cdot \frac{\log (8) \cdot 141.333}{100}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Reorder $\log (8)$ and $141.333$ .

$\frac{0.01}{1.5} \cdot \frac{141.333 \cdot \log (8)}{100}$

Step 1.2.2

Simplify $141.333 \cdot \log (8)$ by moving $141.333$ inside the logarithm.

$\frac{0.01}{1.5} \cdot \frac{\log (8^{141.333})}{100}$

Step 1.3

Factor $0.01$ out of $100$ .

$\frac{0.01}{1.5} \cdot \frac{\log (8^{141.333})}{0.01 (10000)}$

Step 1.4

Cancel the common factor.

$\frac{0.01}{1.5} \cdot \frac{\log (8^{141.333})}{0.01 \cdot 10000}$

Step 1.5

Rewrite the expression.

$\frac{1}{1.5} \cdot \frac{\log (8^{141.333})}{10000}$

Step 2

Multiply $\frac{1}{1.5}$ by $\frac{\log (8^{141.333})}{10000}$ .

$\frac{\log (8^{141.333})}{1.5 \cdot 10000}$

Step 3

Multiply $1.5$ by $10000$ .

$\frac{\log (8^{141.333})}{15000}$

Step 4

Rewrite $\frac{\log (8^{141.333})}{15000}$ as $\frac{1}{15000} \log (8^{141.333})$ .

$\frac{1}{15000} \log (8^{141.333})$

Step 5

Simplify $\frac{1}{15000} \log (8^{141.333})$ by moving $\frac{1}{15000}$ inside the logarithm.

$\log ({(8^{141.333})}^{\frac{1}{15000}})$

Step 6

Multiply the exponents in ${(8^{141.333})}^{\frac{1}{15000}}$ .

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Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log (8^{141.333 (\frac{1}{15000})})$

Step 6.2

Divide $1$ by $15000$ .

$\log (8^{141.333 \cdot 0.0000\overline{6}})$

Step 6.3

Multiply $141.333$ by $0.0000\overline{6}$ .

$\log (8^{0.0094222})$

Step 7

Raise $8$ to the power of $0.0094222$ .

$\log (1.01978611)$

Step 8

Log base $10$ of $1.01978611$ is approximately $0.00850909$ .

$0.00850909$