We can use the fact that 32 is equal to 2 raised to the power of 5:
32 = 2^5
Substituting this into the equation gives:
16^x = 2^5
We can then rewrite 16 as 2^4, since 16 is equal to 2 raised to the power of 4:
(2^4)^x = 2^5
Simplifying the left side of the equation gives:
2^(4x) = 2^5
Now we can see that the bases of both sides of the equation are equal, so we can set the exponents equal to each other:
4x = 5
Dividing both sides by 4 gives:
x = 5/4
Therefore, the solution to the equation 16^x = 32 is x = 5/4.