Precalculus Examples

$\log (\log (10000^{2 x}))$

Step 1

Expand $\log (10000^{2 x})$ by moving $2 x$ outside the logarithm.

$\log (2 x \log (10000))$

Step 2

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

$\log (2 x \cdot 4)$

Step 3

Multiply $4$ by $2$ .

$\log (8 x)$

Step 4

Rewrite $\log (8 x)$ as $\log (8) + \log (x)$ .

$\log (8) + \log (x)$

Step 5

Simplify each term.

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Step 5.1

Rewrite $\log (8)$ as $\log (2^{3})$ .

$\log (2^{3}) + \log (x)$

Step 5.2

Expand $\log (2^{3})$ by moving $3$ outside the logarithm.

$3 \log (2) + \log (x)$