Trigonometry Examples

$\log_{8} (40)$

Step 1

Rewrite $\log_{8} (40)$ as $\log_{8} (2^{3} \cdot 5)$ .

$\log_{8} (2^{3} \cdot 5)$

Step 2

Rewrite $\log_{8} (2^{3} \cdot 5)$ as $\log_{8} (2^{3}) + \log_{8} (5)$ .

$\log_{8} (2^{3}) + \log_{8} (5)$

Step 3

Simplify each term.

Tap for more steps...

Step 3.1

Expand $\log_{8} (2^{3})$ by moving $3$ outside the logarithm.

$3 \log_{8} (2) + \log_{8} (5)$

Step 3.2

Logarithm base $8$ of $2$ is $\frac{1}{3}$ .

$3 (\frac{1}{3}) + \log_{8} (5)$

Step 3.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.3.1

Cancel the common factor.

$3 (\frac{1}{3}) + \log_{8} (5)$

Step 3.3.2

Rewrite the expression.

$1 + \log_{8} (5)$