SOLUTION: Find the solution(s) to {{{2^k=sqrt(3^(k-2))}}} How do I get rid of the square root? Is that the first step? I'm not sure...

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the solution(s) to {{{2^k=sqrt(3^(k-2))}}} How do I get rid of the square root? Is that the first step? I'm not sure...      Log On


   

Question 674115: Find the solution(s) to 2%5Ek=sqrt%283%5E%28k-2%29%29
How do I get rid of the square root? Is that the first step? I'm not sure...
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2%5Ek=sqrt%283%5E%28k-2%29%29
Square both sides
4%5Ek+=+3%5E%28k-2%29
k*log(4) = (k-2)*log(3) = k*log(3) - 2log(3)
k*log(4) - k*log(3) = -2log(3)
k(log(3) - log(4)) = log(9)
k*log(3/4) = log(9)
k = log(9)/log(0.75)
k =~ -7.63768