SOLUTION: 2 * 3^2x = 5 (The exponent on 3 is 2x.) I have the answer for this question but I do not understand how to do it. Could you please provide me with the steps with an explanation.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 2 * 3^2x = 5 (The exponent on 3 is 2x.) I have the answer for this question but I do not understand how to do it. Could you please provide me with the steps with an explanation.      Log On


   

Question 925851: 2 * 3^2x = 5 (The exponent on 3 is 2x.)
I have the answer for this question but I do not understand how to do it. Could you please provide me with the steps with an explanation. Thanks!
Found 2 solutions by ankor@dixie-net.com, MathLover1:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
2+%2A+3%5E%282x%29+=+5+
divide both sides by 2
3%5E%282x%29+=+2.5+
use logs here
log%28%283%5E%282x%29%29%29+=+log%28%282.5%29%29+
the log equiv of exponents
2x*log(3) = log(2.5)
2x = log%28%282.5%29%29%2Flog%28%283%29%29
using a calc we have
2x = .834
x = .834/2
x = .417
:
:
confirm this on your calc enter 2 * 3^(2*.417)

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
2+%2A+3%5E%282x%29+=+5
3%5E%282x%29+=+5%2F2...use logarithm

log%283%5E%282x%29%29+=+log%285%2F2%29

x%2Alog%283%5E2%29+=+log%285%29-log%282%29

x+=+%28log%285%29-log%282%29%29%2Flog%289%29

x+=+%28log%285%29-log%282%29%29%2Flog%283%5E2%29

x+=+%28log%285%29-log%282%29%29%2F2log%283%29

x+=+%280.698970004336-0.30102999566398%29%2F%282%2A0.4771212547%29

x=0.417