Precalculus Examples

$\log_{5} (8 x) - \log_{5} (4)$

Step 1

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

$\log_{5} (\frac{8 x}{4})$

Step 2

Cancel the common factor of $8$ and $4$ .

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Step 2.1

Factor $4$ out of $8 x$ .

$\log_{5} (\frac{4 (2 x)}{4})$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $4$ .

$\log_{5} (\frac{4 (2 x)}{4 (1)})$

Step 2.2.2

Cancel the common factor.

$\log_{5} (\frac{4 (2 x)}{4 \cdot 1})$

Step 2.2.3

Rewrite the expression.

$\log_{5} (\frac{2 x}{1})$

Step 2.2.4

Divide $2 x$ by $1$ .

$\log_{5} (2 x)$