Precalculus Examples

$\frac{\log (12) - \log (4)}{\log (15) + \log (5)}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

$\frac{\log (\frac{12}{4})}{\log (15) + \log (5)}$

Step 1.2

Divide $12$ by $4$ .

$\frac{\log (3)}{\log (15) + \log (5)}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\log (3)}{\log (15 \cdot 5)}$

Step 2.2

Multiply $15$ by $5$ .

$\frac{\log (3)}{\log (75)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (3)}{\log (75)}$

Decimal Form:

$0.25445635 \dots$