SOLUTION: solve the equation for x and express irrational solution in exact form 3^(x^2)*27=9^(2x)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve the equation for x and express irrational solution in exact form 3^(x^2)*27=9^(2x)      Log On


   

Question 381495: solve the equation for x and express irrational solution in exact form
3^(x^2)*27=9^(2x)
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
solve for x and express irrational in exact form
2 log(base a)(x-4)=log(base a)^18+log(base a)^2
---
2loga(x-4)-loga(sqrt(18)) + loga(sqrt(2))
-----
= loga[(x-4)^2*2/sqrt(18)]
===
= logz[2(x-4)^2/sqrt(18)]
===============================
Cheers,
Stan H.

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi

Solving for x

  3%5E%28x%5E2%29%2A27=9%5E%282x%29

   %283%5E4%29%5E%28x%5E2%29=+%283%5E2%29%5E%282x%29

  %28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29

  3%5E%284%2Ax%5E2%29=3%5E%284x%29

     4x^2 = 4x

    4x^2 - 4x = 0

    4x(x - 1) = 0

      x = 0

     (x - 1) = 0

      x = 1

 CHECKING the Answers

   0 = 0

  3*27 = 81 = 9^2