Precalculus Examples

$\frac{\log (8)}{6 \log (1.07)}$

Step 1

Rewrite $\log (8)$ as $\log (2^{3})$ .

$\frac{\log (2^{3})}{6 \log (1.07)}$

Step 2

Expand $\log (2^{3})$ by moving $3$ outside the logarithm.

$\frac{3 \log (2)}{6 \log (1.07)}$

Step 3

Cancel the common factor of $3$ and $6$ .

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Step 3.1

Factor $3$ out of $3 \log (2)$ .

$\frac{3 (\log (2))}{6 \log (1.07)}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $6 \log (1.07)$ .

$\frac{3 (\log (2))}{3 (2 \log (1.07))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 \log (2)}{3 (2 \log (1.07))}$

Step 3.2.3

Rewrite the expression.

$\frac{\log (2)}{2 \log (1.07)}$

Step 4

Simplify $2 \log (1.07)$ by moving $2$ inside the logarithm.

$\frac{\log (2)}{\log ({1.07}^{2})}$

Step 5

Simplify the denominator.

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Step 5.1

Raise $1.07$ to the power of $2$ .

$\frac{\log (2)}{\log (1.1449)}$

Step 5.2

Log base $10$ of $1.1449$ is approximately $0.05876755$ .

$\frac{\log (2)}{0.05876755}$

Step 6

Log base $10$ of $2$ is approximately $0.30102999$ .

$\frac{0.30102999}{0.05876755}$

Step 7

Divide $0.30102999$ by $0.05876755$ .

$5.12238417$