Write the expression as a single logarithm.
\[
2 \log _{3}(x+3)-\log _{3}(x-20)-\log _{3}(x-9)
\]
\[
2 \log _{3}(x+3)-\log _{3}(x-20)-\log _{3}(x-9)=
\]
(Simplify your answer.)
Answer
So, the expression \(2 \log _{3}(x+3)-\log _{3}(x-20)-\log _{3}(x-9)\) can be written as a single logarithm as \(\boxed{\log _{3}\left(\frac{(x+3)^2}{(x-20)(x-9)}\right)}\)
Step 1 ：Rewrite the expression using the property of logarithms a*log_b(c) = log_b(c^a): \(\log _{3}((x+3)^2)-\log _{3}(x-20)-\log _{3}(x-9)\)
Step 2 ：Simplify the expression using the property of logarithms log_b(c) - log_b(d) = log_b(c/d): \(\log _{3}\left(\frac{(x+3)^2}{(x-20)(x-9)}\right)\)
Step 3 ：So, the expression \(2 \log _{3}(x+3)-\log _{3}(x-20)-\log _{3}(x-9)\) can be written as a single logarithm as \(\boxed{\log _{3}\left(\frac{(x+3)^2}{(x-20)(x-9)}\right)}\)
