Expand the Logarithmic Expression log of log of 100^(50x)

$\log (\log (100^{50 x}))$

Step 1

Expand $\log (100^{50 x})$ by moving $50 x$ outside the logarithm.

$\log (50 x \log (100))$

Step 2

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

$\log (50 x \cdot 2)$

Step 3

Multiply $2$ by $50$ .

$\log (100 x)$

Step 4

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

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

Step 5

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

$2 + \log (x)$