Precalculus Examples

$\frac{2 \log (8)}{\log (8) - 3 \log (5)}$

Step 1

Simplify $2 \log (8)$ by moving $2$ inside the logarithm.

$\frac{\log (8^{2})}{\log (8) - 3 \log (5)}$

Step 2

Simplify the denominator.

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Step 2.1

Simplify $- 3 \log (5)$ by moving $3$ inside the logarithm.

$\frac{\log (8^{2})}{\log (8) - \log (5^{3})}$

Step 2.2

Raise $5$ to the power of $3$ .

$\frac{\log (8^{2})}{\log (8) - \log (125)}$

Step 2.3

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$\frac{\log (8^{2})}{\log (\frac{8}{125})}$

Step 3

Raise $8$ to the power of $2$ .

$\frac{\log (64)}{\log (\frac{8}{125})}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (64)}{\log (\frac{8}{125})}$

Decimal Form:

$- 1.51294159 \dots$