Precalculus Examples

$\log_{3} (100) - \log_{3} (18) - \log_{3} (50)$

Step 1

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

$\log_{3} (\frac{100}{18}) - \log_{3} (50)$

Step 2

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

$\log_{3} (\frac{\frac{100}{18}}{50})$

Step 3

Cancel the common factor of $100$ and $18$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $100$ .

$\log_{3} (\frac{\frac{2 (50)}{18}}{50})$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $18$ .

$\log_{3} (\frac{\frac{2 \cdot 50}{2 \cdot 9}}{50})$

Step 3.2.2

Cancel the common factor.

$\log_{3} (\frac{\frac{2 \cdot 50}{2 \cdot 9}}{50})$

Step 3.2.3

Rewrite the expression.

$\log_{3} (\frac{\frac{50}{9}}{50})$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$\log_{3} (\frac{50}{9} \cdot \frac{1}{50})$

Step 5

Cancel the common factor of $50$ .

Tap for more steps...

Step 5.1

Cancel the common factor.

$\log_{3} (\frac{50}{9} \cdot \frac{1}{50})$

Step 5.2

Rewrite the expression.

$\log_{3} (\frac{1}{9})$

Step 6

Logarithm base $3$ of $\frac{1}{9}$ is $- 2$ .

$- 2$