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Solve the equation 10^x = 100.

The solution to the equation 10^x = 100 is x = 2.

To solve this equation, we need to use logarithms. Taking the logarithm of both sides of the equation, we get:

log(10^x) = log(100)

Using the power rule of logarithms, we can simplify the left-hand side of the equation:

x log(10) = log(100)

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

x = log(100)

Using the definition of logarithms, we know that log(100) is the exponent to which 10 must be raised to get 100. In other words, log(100) = 2, since 10^2 = 100. Therefore, the solution to the equation 10^x = 100 is x = 2.

We can check our answer by plugging it back into the original equation:

10^2 = 100

This is true, so our solution is correct.

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