Precalculus Examples

$\frac{\ln (100)}{\ln (3)} - 1$

Step 1

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{\ln (3)}{\ln (3)}$ .

$\frac{\ln (100)}{\ln (3)} - 1 \cdot \frac{\ln (3)}{\ln (3)}$

Step 2

Combine $- 1$ and $\frac{\ln (3)}{\ln (3)}$ .

$\frac{\ln (100)}{\ln (3)} + \frac{- \ln (3)}{\ln (3)}$

Step 3

Combine the numerators over the common denominator.

$\frac{\ln (100) - \ln (3)}{\ln (3)}$

Step 4

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

$\frac{\ln (\frac{100}{3})}{\ln (3)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (\frac{100}{3})}{\ln (3)}$

Decimal Form:

$3.19180654 \dots$