Solve for L L=10 log of (10^-9)/(10^-12)

$L = 10 \log (\frac{10^{- 9}}{10^{- 12}})$

Step 1

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

$L = 10 \log (10^{- 9} \cdot 10^{12})$

Step 2

Multiply $10^{- 9}$ by $10^{12}$ by adding the exponents.

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

$L = 10 \log (10^{- 9 + 12})$

Add $- 9$ and $12$ .

$L = 10 \log (10^{3})$

Step 3

Use logarithm rules to move $3$ out of the exponent.

$L = 10 (3 \log (10))$

Step 4

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

$L = 10 (3 \cdot 1)$

Step 5

Multiply $3$ by $1$ .

$L = 10 \cdot 3$

Step 6

Multiply $10$ by $3$ .

$L = 30$