SOLUTION: Find the exact solution to the exponential equation 2000=20(3)^(2x). (Do not give a decimal approximation.) x=????????? Thanks!

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the exact solution to the exponential equation 2000=20(3)^(2x). (Do not give a decimal approximation.) x=????????? Thanks!       Log On


   

Question 999351: Find the exact solution to the exponential equation 2000=20(3)^(2x). (Do not give a decimal approximation.)
x=?????????
Thanks!

Found 2 solutions by fractalier, Alan3354:
Answer by fractalier(6550) About Me  (Show Source):
You can put this solution on YOUR website!
From
2000=20(3)^(2x)
we divide by 20 first...
100 = 3^(2x)
then take log-to-the-base-three
log(3)100 = 2x
and divide by 2, so that
x = (1/2)log(3)100

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the exact solution to the exponential equation 2000=20(3)^(2x).
----
2000=20(3)^(2x)
100 = 3^(2x)
2x*log(3) = log(100) = 2
x = 1/log(3)