Show how an efficient algorithm for computing discrete logarithms with base a can be used to efficiently compute discrete logarithms with base b I have an exercise that says the following:
Let $p$ be an odd prime, and let $a$ and $b$ be generators $\mathbb{Z}​_p^*$. Suppose that we have an efficient algorithm $A$ for computing discrete logarithms with base $a$. Show how this algorithm can be used to efficiently compute discrete logarithms with base $b$.
With considering a change of base rule, I have done the following:
B(b,x):
    return A(x) / A(b)

Is this correct and the end of the exercise? I would say that it is, but this is very easy compared to the other exercise I'm currently solving, so I think that I have missed something...
Is this correct and the end of the exercise?

I can't say to what extent your professor wants you to be explicit, but it is essentially correct (and I'd accept it as an answer if I were grading it).  Now, your professor may be expecting you to explain (or give a proof) why this is correct.