Solve for L L=10 log of (10^-1)/(10^-12)

$L = 10 \log (\frac{10^{- 1}}{10^{- 12}})$

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

$L = 10 \log (10^{- 1} \cdot 10^{12})$

Multiply $10^{- 1}$ by $10^{12}$ by adding the exponents.

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

$L = 10 \log (10^{- 1 + 12})$

Add $- 1$ and $12$ .

$L = 10 \log (10^{11})$

Use logarithm rules to move $11$ out of the exponent.

$L = 10 (11 \log (10))$

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

$L = 10 (11 \cdot 1)$

Multiply $11$ by $1$ .

$L = 10 \cdot 11$

Multiply $10$ by $11$ .

$L = 110$