### Instruction: If $\log_5 (x+4)=3$, find $\log_{11} x$.### Response: To solve for $x$, I need to undo the logarithm function by raising both sides of the equation to the base 5.
This gives me $5^{\log_5 (x+4)}=5^3$.
By the property of logarithms, the left-hand side simplifies to $x+4$.
So I have $x+4=125$.
Subtracting 4 from both sides, I get $x=121$.
Now that I have $x$, I can plug it into $\log_{11} x$.
This is the same as asking what power of 11 gives me 121.
I notice that $11^2=121$, so the answer must be 2.