Solve for l l=10 log of (10^-3)/(10^-12)

$l = 10 \log (\frac{10^{- 3}}{10^{- 12}})$

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

$l = 10 \log (10^{- 3} \cdot 10^{12})$

Multiply $10^{- 3}$ by $10^{12}$ by adding the exponents.

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

$l = 10 \log (10^{- 3 + 12})$

Add $- 3$ and $12$ .

$l = 10 \log (10^{9})$

Use logarithm rules to move $9$ out of the exponent.

$l = 10 (9 \log (10))$

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

$l = 10 (9 \cdot 1)$

Multiply $9$ by $1$ .

$l = 10 \cdot 9$

Multiply $10$ by $9$ .

$l = 90$