Exponential Equation In Quadratic Form

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SUMMARY

The discussion focuses on solving the exponential equation 3^(2x) + 3^(x+1) - 4 = 0 by using substitution. The key substitution is u = 3^x, transforming the equation into a quadratic form: au² + bu + c = 0. The middle term 3^(x+1) is expressed as 3^x * 3^1, simplifying the equation. After transforming it into quadratic form, users are advised to solve for u using factorization or the quadratic formula, followed by substituting back to find x.

PREREQUISITES
  • Understanding of exponential equations
  • Familiarity with quadratic equations
  • Knowledge of substitution methods in algebra
  • Ability to apply the quadratic formula
NEXT STEPS
  • Practice solving exponential equations using substitution
  • Learn about the quadratic formula and its applications
  • Explore factorization techniques for quadratic equations
  • Study the properties of exponential functions
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Students studying algebra, particularly those tackling exponential and quadratic equations, as well as educators looking for effective teaching methods in these topics.

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 [tex]au^2+bu+c=0[/tex] 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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