PLEASE USE GROUPING SYMBOLS to make clear what you mean.
I think you mean
[MATH]A = \sqrt{2} * 0.5^{(2t - 2.5)}[/MATH]
If that is what you meant, but did not write, here is a big hint: why might it make sense to take logarithms with base 2 of both sides of the equation?
Assuming you mean A = sqrt(2)*(0.5)^(2t-2.5), observe, in addition to Jomo's comments, that sqrt(2) = 2^(1/2) and that (x^m)^n = x^(mn) and x^-n = 1/x^n.
So you have A = (2)^(1/2)*(1/2)^(2t - 5/2). Now expand the right-hand side. Show us whatever you can do, so we can help you through the next step.
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