logarithmic equations

[Aisha01]

How do I turn the equation A= √2•0.5^2t-2.5 into A=8•(1/4) ^t ?

 

[JeffM]

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?

 

[Steven G]

0.5 = 1/2

x^a-b= x^a/x^b

 

[Dr.Peterson]

How do I turn the equation A= √2•0.5^2t-2.5 into A=8•(1/4) ^t ?

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.