f(x)= log8 (x + 9)^2
No.
Realize that $\displaystyle \left( {x + 9} \right)^2 = \left| {x + 9} \right|^2 $.
Of course, your answer is correct if the problem means $\displaystyle \left[ {\log _8 \left( {x + 9} \right)} \right]^2.$
That is the way most computer algebra systems would read it.
But I don't think that is what was meant.