Precalculus Examples

$\frac{\log (81)}{\log (3)} - \frac{\log (3)}{\log (3)}$

Step 1

Combine the numerators over the common denominator.

$\frac{\log (81) - \log (3)}{\log (3)}$

Step 2

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

$\frac{\log (\frac{81}{3})}{\log (3)}$

Step 3

Divide $81$ by $3$ .

$\frac{\log (27)}{\log (3)}$

Step 4

Rewrite $\log (27)$ as $\log (3^{3})$ .

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

Step 5

Expand $\log (3^{3})$ by moving $3$ outside the logarithm.

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

Step 6

Cancel the common factor of $\log (3)$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Divide $3$ by $1$ .

$3$