A Beautiful Exponential Equation | Can You Solve This?

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[krwada]

This problem is very easy for a computer programmer.

One has to understand that both 8 and 32 can be represented as a power of 2.

8^x = 32

This can be re-written as:
2^(3x) = 2^5

Now, the above expression is all in base-2.
Thus we need to solve the following for x.

3x = 5 --> x = 5/3 =

[thomasharding]

X to the Y power = Z => Log Z / Log X =Y 8 to the 1.66667 power = 32 Thank you for the brain exercise.

[Pendergast]

I took the base-2-log of both sides, movign the x down giving X log2 (8) = log2 (32) which gives 3X = 5, therefore X = 5/3 ~ 1.6667