Precalculus Examples

$\log_{5} (150)$

Step 1

Rewrite $\log_{5} (150)$ as $\log_{5} (2 \cdot 3 \cdot 5^{2})$ .

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

Step 2

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

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

Step 3

Use logarithm rules to move $2$ out of the exponent.

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

Step 4

Logarithm base $5$ of $5$ is $1$ .

$\log_{5} (2 \cdot 3) + 2 \cdot 1$

Step 5

Multiply $2$ by $1$ .

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

Step 6

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

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