Exponential Equation In Quadratic Form

AI Thread Summary
To solve the equation 3^(2x) + 3^(x+1) - 4 = 0, a substitution is necessary, specifically letting u = 3^x. This transforms the equation into a quadratic form, allowing for easier manipulation. The term 3^(x+1) can be rewritten as 3^x * 3, which aids in forming the quadratic equation. After substituting and arranging the equation into the standard form au^2 + bu + c = 0, the next step is to solve for u using either factorization or the quadratic formula. Finally, substitute back to find the value of x.
chillfactor
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Homework Statement


The problem is 3^2x+3^(x+1)-4=0

I know I had to solve it by substitution


Homework Equations





The Attempt at a Solution


I had u = 3^x
I put it in:
(u )(u ), but I was not sure how to get the middle term 3^(x+1)
 
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You could write 3^(x+1) = 3^x * 3^1
 
chillfactor, that's a bad way to do it. Take this slowly, step by step.
First make the substitution, then once it is in the general quadratic form au^2+bu+c=0 THEN solve for u either by factorizing or using the quadratic formula. After doing that, substitute back in and solve for x.
 
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