Answer: The solution is x = 3.
Step-by-step explanation: We are given to solve the following logarithmic equation:
\(\log 3(x+12)=\log 3(5x).\)
We will be using the following property of logarithm:
\((i)~\log(ab)=\log a+\log b\\\\(ii)~\log a=\log b~~~\Rightarrow a=b.\)
We have
\(\log 3(x+12)=\log 3(5x)\\\\\Rightarrow \log3+\log(x+12)=\log 3+\log 5x\\\\\Rightarrow \log(x+12)=\log 5x\\\\\Rightarrow x+12=5x\\\\\Rightarrow 5x-x=12\\\\\Rightarrow 4x=12\\\\\Rightarrow x=3.\)
Thus, the solution of the given equation is x = 3.
