SOLUTION: Solve for x: 2^2x - 3 * 2^x - 40 = 0

Algebra ->  Expressions-with-variables -> SOLUTION: Solve for x: 2^2x - 3 * 2^x - 40 = 0      Log On


   

Question 481620: Solve for x:
2^2x - 3 * 2^x - 40 = 0
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
2%5E%282x%29-3%2A2%5Ex-40=0, substituting 2%5Ex=y we get the quadratic equation:
y%5E2-3y-40=0. We solve this equation by factoring:%28y-8%29%28y%2B5%29=0
The roots are: {-5, 8}. Now we find the roots of original equation:
2%5Ex=8<=>x=3 and 2%5Ex=-5<=>x%2Aln2=ln%28-5%29, since the log of
negative numbers doesn't exist our equation has only one solution x=3.