SOLUTION: solve each equation. Round to four decimal places. 2^n=sqrt(3^n-2)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: solve each equation. Round to four decimal places. 2^n=sqrt(3^n-2)      Log On


   

Question 570869: solve each equation. Round to four decimal places.
2^n=sqrt(3^n-2)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2%5En=sqrt%283%5E%28n-2%29%29
Square both sides
2%5E%282n%29+=+3%5E%28n-2%29 assuming n-2 is the exponent. Use parentheses.
2n*log(2) = (n-2)*log(3) = nlog(3) - log(9)
2n*log(2) - n*log(3) = -log(9)
n*(log(3) - 2log(2)) = log(9)
n = log(9)/log(3/4)
n =~ -7.6377