Expand the Logarithmic Expression log of log of 100^(500x)

$\log (\log (100^{500 x}))$

Step 1

Expand $\log (100^{500 x})$ by moving $500 x$ outside the logarithm.

$\log (500 x \log (100))$

Step 2

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

$\log (500 x \cdot 2)$

Step 3

Multiply $2$ by $500$ .

$\log (1000 x)$

Step 4

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

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

Step 5

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

$3 + \log (x)$