If $\log_5 (x+4)=3$, find $\log_{11} x$.
First, I rewrite the given equation in exponential form: $x+4=5^3$. Then, I simplify the right-hand side: $x+4=125$. Next, I isolate $x$ by subtracting $4$ from both sides: $x=121$. Now, I have the value of $x$, so I can plug it into the expression I want to find: $\log_{11} x$. This means I need to find the exponent that makes $11$ equal to $121$. I can use trial and error, or I can notice that $121=11^2$, so the exponent must be $2$. Therefore, $\log_{11} x=2$. 