Is this correct for this question?

For question three -
log⁡ab = t , which means b =a^t.
Then, 
b^y = (a^t)^y
because (a^t)^y = a^ty
by the power of a power rule.
Now, apply the logarithm b^y:
log⁡ab^y = loga a^ty = ty = y logab
because
loga a^x = x
Since log⁡ab = t , we can replace t with log⁡ab:
ty = y⋅log⁡ab
Therefore, log⁡a(b^y) = y⋅log⁡ab is proven.