Algebra Examples

$\log_{14} (6) - \log_{14} (\frac{3}{2})$

Step 1

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

$\log_{14} (\frac{6}{\frac{3}{2}})$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\log_{14} (6 (\frac{2}{3}))$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Factor $3$ out of $6$ .

$\log_{14} (3 (2) \frac{2}{3})$

Step 3.2

Cancel the common factor.

$\log_{14} (3 \cdot 2 \frac{2}{3})$

Step 3.3

Rewrite the expression.

$\log_{14} (2 \cdot 2)$

Step 4

Multiply $2$ by $2$ .

$\log_{14} (4)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\log_{14} (4)$

Decimal Form:

$0.52529907 \dots$