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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
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