Algebra Examples

log (2) - log (8)

$\log (2) - \log (8)$

Step 1

Use the quotient property of logarithms,

{log}_{b} (x) - {log}_{b} (y) = {log}_{b} (\frac{x}{y})

$\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

log (\frac{2}{8})

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

Step 2

Cancel the common factor of

2

$2$ and

8

$8$ .

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Step 2.1

Factor

2

$2$ out of

2

$2$ .

log (\frac{2 (1)}{8})

$\log (\frac{2 (1)}{8})$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor

2

$2$ out of

8

$8$ .

log (\frac{2 \cdot 1}{2 \cdot 4})

$\log (\frac{2 \cdot 1}{2 \cdot 4})$

Step 2.2.2

Cancel the common factor.

$\log (\frac{2 \cdot 1}{2 \cdot 4})$

Step 2.2.3

Rewrite the expression.

$\log (\frac{1}{4})$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\log (\frac{1}{4})$

Decimal Form:

$- 0.60205999 \dots$

$\log 2 - \log 8$

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