Precalculus Examples

$\log_{4} (2) + \log_{4} (10) - \log_{4} (20)$

Step 1

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

$\log_{4} (2 \cdot 10) - \log_{4} (20)$

Step 2

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

$\log_{4} (\frac{2 \cdot 10}{20})$

Step 3

Cancel the common factor of $2$ and $20$ .

Tap for more steps...

Step 3.1

Factor $2$ out of $2 \cdot 10$ .

$\log_{4} (\frac{2 (10)}{20})$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $2$ out of $20$ .

$\log_{4} (\frac{2 \cdot 10}{2 \cdot 10})$

Step 3.2.2

Cancel the common factor.

$\log_{4} (\frac{2 \cdot 10}{2 \cdot 10})$

Step 3.2.3

Rewrite the expression.

$\log_{4} (\frac{10}{10})$

Step 4

Cancel the common factor of $10$ .

Tap for more steps...

Step 4.1

Cancel the common factor.

$\log_{4} (\frac{10}{10})$

Step 4.2

Rewrite the expression.

$\log_{4} (1)$

Step 5

Logarithm base $4$ of $1$ is $0$ .

$0$