Solve the equation 10^2x = 10000.

The solution to the equation 10^2x = 10000 is x = 2/3.

To solve this equation, we can use logarithms. Taking the logarithm of both sides with base 10, we get:

log(10^2x) = log(10000)

Using the power rule of logarithms, we can bring the exponent 2x down as a coefficient:

2x log(10) = log(10000)

Since log(10) = 1, we can simplify the left-hand side:

2x = log(10000)

Using the logarithm identity log(ab) = log(a) + log(b), we can simplify the right-hand side:

2x = log(10^4)

2x = 4 log(10)

Since log(10) = 1, we can simplify further:

2x = 4

Dividing both sides by 2, we get the solution:

x = 2/3

Therefore, the solution to the equation 10^2x = 10000 is x = 2/3.