Expand the Logarithmic Expression log of log of 100000^(2x)

$\log (\log (100000^{2 x}))$

Expand $\log (100000^{2 x})$ by moving $2 x$ outside the logarithm.

$\log (2 x \log (100000))$

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

$\log (2 x \cdot 5)$

Multiply $5$ by $2$ .

$\log (10 x)$

Rewrite $\log (10 x)$ as $\log (10) + \log (x)$ .

$\log (10) + \log (x)$

Logarithm base $10$ of $10$ is $1$ .

$1 + \log (x)$