SOLUTION: Help me solve these two questions 1. 2^(2x)-5(2^x)+4=0 2. 3^(2x+1)+26(3^x)-9=0

Algebra ->  Exponents -> SOLUTION: Help me solve these two questions 1. 2^(2x)-5(2^x)+4=0 2. 3^(2x+1)+26(3^x)-9=0      Log On


   

Question 1026222: Help me solve these two questions
1. 2^(2x)-5(2^x)+4=0
2. 3^(2x+1)+26(3^x)-9=0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
I will solve #2 for you.
2. 3%5E%282x%2B1%29%2B26%283%5Ex%29-9=0
<==>3%2A3%5E%282x%29%2B26%283%5Ex%29-9=0
<==>%283%2A3%5Ex+-1%29%283%5Ex+%2B9%29+=+0
==> 3%2A3%5Ex+-1=+0 or 3%5Ex+%2B9+=+0
The first equation is equivalent to 3%2A3%5Ex+-1=+0
==> 3%5Ex+=+3%5E%28-1%29 ==> x = -1.
The second equation 3%5Ex+%2B9+=+0 is equivalent to 3%5Ex+=+-9 and as such has no real solution.
Therefore the only (real) solution is x = -1.