Question

Can you prove `a^x * a^y = log(xy)`?

Answer 1

log is for common logarithm. See Socratic graphs for selective values of `a >0`.

Explanation:

a = e:

graph{e^(x+y)-log(xy)=0 [-6.99, 6.996, -3.496, 3.497]} a=10:

a =10:

graph{10^(x+y)-log(xy)=0 [-5, 5, -2.5, 2.5]}

a = 2:

graph{2(x+y)-log(xy)=0 [-1.25, 1.25, -0.625, 0.625]}