求证 log(a) (M·N)=log(a) M+log(a) N

证明：设log(a)(mn)=k 则有：a^k=mn
log(a)m=x 则有：a^x=m
log(a)n=y 则有：a^y=n
可得：mn=a^x*a^y=a^(x+y)=a^k
即：k=x+y
得：log(a)(mn)=log(a)m+log(a)n很精彩，请问老师如何求证 a^x*a^y=a^(x+y)?