Expand the Logarithmic Expression log of log of 10000^(25x)

$\log (\log (10000^{25 x}))$

Step 1

Expand $\log (10000^{25 x})$ by moving $25 x$ outside the logarithm.

$\log (25 x \log (10000))$

Step 2

Logarithm base $10$ of $10000$ is $4$ .

$\log (25 x \cdot 4)$

Step 3

Multiply $4$ by $25$ .

$\log (100 x)$

Step 4

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

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

Step 5

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

$2 + \log (x)$