Expand the Logarithmic Expression log of log of 100000^(200x)

$\log (\log (100000^{200 x}))$

Step 1

Expand $\log (100000^{200 x})$ by moving $200 x$ outside the logarithm.

$\log (200 x \log (100000))$

Step 2

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

$\log (200 x \cdot 5)$

Step 3

Multiply $5$ by $200$ .

$\log (1000 x)$

Step 4

Rewrite $\log (1000 x)$ as $\log (1000) + \log (x)$ .

$\log (1000) + \log (x)$

Step 5

Logarithm base $10$ of $1000$ is $3$ .

$3 + \log (x)$