2^n-1=8^n, n=?

Or do you mean  

$$2^{n-1}=8^n$$

in which case, because 8 = 2³

$$2^{n-1} = 2^{3n}$$

so n-1 = 3n 

-1 = 2n

n = -1/2

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No solution!

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(However, 8ⁿ - 1 = 2ⁿ does have a solution.)