How do you solve 4 to the power of x equals 128?

Answer 1

3-2

Answer 2

If we take the logarithm of both sides, then it is log(4^x) = log(128). Then from logarithm rules, this can be changed to: x*log(4) = log(128), then x = log(128)/log(4). You can punch this into a calculator and get the answer, but what if we use log base 2, we don't need a calculator. So log2(4) = 2, because 2² = 4. And log2(128) = 7, because 2^7 = 128. So we have x = 7/2 = 3.5, then you can check your answer: 4^3.5 = (4^3)*(4^.5). So 4 cubed = 64, and 4 raised to the 1/2 power is the square root of 4, which is 2. So 64 times 2 = 128.