Precalculus Examples

$\log (\log ({(100000)}^{10000}))$

Step 1

Expand $\log ({(100000)}^{10000})$ by moving $10000$ outside the logarithm.

$\log (10000 \log (100000))$

Step 2

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

$\log (10000 \cdot 5)$

Step 3

Multiply $10000$ by $5$ .

$\log (50000)$

Step 4

Rewrite $\log (50000)$ as $\log (2^{4} \cdot 5^{5})$ .

$\log (2^{4} \cdot 5^{5})$

Step 5

Rewrite $\log (2^{4} \cdot 5^{5})$ as $\log (2^{4}) + \log (5^{5})$ .

$\log (2^{4}) + \log (5^{5})$

Step 6

Simplify each term.

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Step 6.1

Expand $\log (2^{4})$ by moving $4$ outside the logarithm.

$4 \log (2) + \log (5^{5})$

Step 6.2

Expand $\log (5^{5})$ by moving $5$ outside the logarithm.

$4 \log (2) + 5 \log (5)$