Question 1040053

3^2x - 3^x+1 +2 = 0
We can rewrite this equation
3^2x +2 = 3^x+1 This helps us to see everything in positive term

If both sides of the equal sign are equal then the log of both sides has to be equal. We find the log of both sides. This helps us to get rid of the exponent which is causing problem

log(3^2x +2) = log(3^x+1)
Using log properties we will have 
log(3^2x +  2) = log(3^x+1)

log3^2x  + log2 =  log3^(x+1)
using log properties
2xlog3+ log2 = (x+1)log3

Using calculator to find the log of 2 and 3

2x(.477) + .301 = (x+1)(.477)
It is a simple equation that we have to find x
2.862x + .301 = .477x +.477

Therefore:
2.862x + .477x  =  .477 -.301
3.339x = .176
x= .176/3.39
x= .052