Consider the expression $\log\mathopen{}\left(\frac{A}{B}\right)\mathclose{}$ Use a negative exponent on $B$ to rewrite the fraction inside the log function as a product. $\log\mathopen{}\left(\frac{A}{B}\right)\mathclose{}=\log\Big($$\Big)$ The right side of the equation is now a product of two values. Use the rule $\log(A\cdot B)=\log(A)+\log(B)$ to rewrite the right side as the sum of two log terms. $\log(AB^{-1})=$$+$ The second term on the right side has a value with a negative exponent. Use the rule $\log_{b}(N^{x})=x \log_{b}(N)\text{,}$ where $b>0\text{,}$ to bring down the negative exponent. Now the second term is simply “adding a negative”. Rewrite the right side after the negative exponent is brought down in front of the $log$ term. $\log(AB^{-1})=$$+$ The entire right side can now be written as a difference (subtraction).