SOLUTION: Solve the equation 3^2x = 7(3^x)- 12. write final solution as exact or in form of x= log(base a)b *Would I take the logs of both sides and then use log properties?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the equation 3^2x = 7(3^x)- 12. write final solution as exact or in form of x= log(base a)b *Would I take the logs of both sides and then use log properties?       Log On


   

Question 556328: Solve the equation 3^2x = 7(3^x)- 12. write final solution as exact or in form of x= log(base a)b
*Would I take the logs of both sides and then use log properties?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the equation 3^2x = 7(3^x)- 12
**
7(3^x)-3^2x=12
factor out 3^x
(3^x)(7-3^x)=12
take log of both sides:
log(3^x)+log(7-3^x)=log(12)=1.0792
log[(3^x)(7-3^x)]=1.0792
convert to exponential form:
10^1.0792=(3^x)(7-3^x)=7(3^x)-3^2x=12
7(3^x)-3^2x-12=0
let u=3^x
u^2=3^2x
u^2-7u+12=0
(u-4)(u+3)=0
u=-3≠3^x (reject)
or
u=4=3^x
xlog3=log4
x=log4/log3≈1.2619.. (ans)