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1 solution
Sorry for the formating.
Let lg be log base 2
The sum of a geometric is standard; in this case the sum is 1/4
Since 1.25 is 5/4: Log base 1.25 of 1/4 is lg(1/4) / lg(1.25) = -2/(lg(5) - 2)
Call this value x
By definition of log:
0.64 = 2^lg(0.64) = 2^lg(16/25) = 2^(lg16 - lg25) = 2^(4 - 2lg5)
So 0.64^x is
2^(-2(4 - 2lg5)/(lg(5) - 2)) = 2^(4(lg5 - 2)/(lg5 - 2)) = 2^4 = 16