SOLUTION: Find the solution of the exponential equation: 2^(2x+5) = 3^(x−48) in terms of logarithms. THANKS TO ANYONE WHO COULD HELP!!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the solution of the exponential equation: 2^(2x+5) = 3^(x−48) in terms of logarithms. THANKS TO ANYONE WHO COULD HELP!!      Log On


   

Question 139456: Find the solution of the exponential equation:
2^(2x+5) = 3^(x−48)
in terms of logarithms.
THANKS TO ANYONE WHO COULD HELP!!
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
taking log __ (2x+5)log(2)=(x-48)log(3)

distributing __ 2xlog(2)+5log(2)=xlog(3)-48log(3)

subtracting xlog(3)+5log(2) __ 2xlog(2)-xlog(3)=-48log(3)-5log(2)

factoring __ x[2log(2)-log(3)]=-48log(3)-5log(2)

dividing by 2log(2)-log(3) __ x=[-48log(3)-5log(2)]/[2log(2)-log(3)]