Solve the equation 2^x = 16.

The solution to 2^x = 16 is x = 4.

To solve this equation, we need to use logarithms. Specifically, we need to take the logarithm of both sides of the equation with base 2, since 2 is the base of the exponent in the left-hand side of the equation. This gives us:

log2(2^x) = log2(16)

Using the property of logarithms that states loga(b^c) = c*loga(b), we can simplify the left-hand side of the equation:

x*log2(2) = log2(16)

Since log2(2) = 1, we can simplify further:

x = log2(16)

Now we just need to evaluate log2(16). This means finding the exponent to which we need to raise 2 to get 16. We can do this by repeatedly dividing 16 by 2 until we get 1:

16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1

We divided 4 times, so the exponent we need is 4. Therefore, the solution to the equation 2^x = 16 is x = 4.