Can anyone simplify this logarithmic function?

Question

The function is: $$X^{\log_a(Y)}$$

Thanks

edit: This is from my book. The answer given is y* log (base a) X.

But i cant solve. + I am from mobile and never used this site before sorry for formatting

Answer 1

$$ x^{\log_a y}=(e^{\ln x})^{\log_a y}=e^{\frac{\ln x \ln y}{\ln a}} $$ What else? :|

Answer 2

Using $b^x = e^{\ln(b) \cdot y}$ and $\log_b x = \frac{\log x}{\log b}$:

$X^{\log_a Y} = X^{\frac{\ln Y}{\ln a}} = e^{\frac{\ln X \ln Y}{\ln a}}$

which is clearly symmetric with respect to $X$ and $Y$, so you can do the same computation with $X$ and $Y$ swapped to obtain $Y^{\log_a X}$.