Precalculus Examples

$\log (\log (100000^{20 x}))$

Step 1

Expand $\log (100000^{20 x})$ by moving $20 x$ outside the logarithm.

$\log (20 x \log (100000))$

Step 2

Logarithm base $10$ of $100000$ is $5$ .

$\log (20 x \cdot 5)$

Step 3

Multiply $5$ by $20$ .

$\log (100 x)$

Step 4

Rewrite $\log (100 x)$ as $\log (100) + \log (x)$ .

$\log (100) + \log (x)$

Step 5

Logarithm base $10$ of $100$ is $2$ .

$2 + \log (x)$