Precalculus Examples

$10 \log (\frac{10^{- 2}}{10^{- 12}})$

Step 1

Move $10^{- 12}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$10 \log (10^{- 2} \cdot 10^{12})$

Step 2

Multiply $10^{- 2}$ by $10^{12}$ by adding the exponents.

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Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$10 \log (10^{- 2 + 12})$

Step 2.2

Add $- 2$ and $12$ .

$10 \log (10^{10})$

Step 3

Use logarithm rules to move $10$ out of the exponent.

$10 (10 \log (10))$

Step 4

Logarithm base $10$ of $10$ is $1$ .

$10 (10 \cdot 1)$

Step 5

Multiply $10$ by $1$ .

$10 \cdot 10$

Step 6

Multiply $10$ by $10$ .

$100$