SOLUTION: Find all solutions to the equation 3 * 9^t - 82 * 3^t + 27 = 0

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find all solutions to the equation 3 * 9^t - 82 * 3^t + 27 = 0      Log On


   

Question 803291: Find all solutions to the equation 3 * 9^t - 82 * 3^t + 27 = 0
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Let's call 3%5Et by a shorter name, with the change of variable
x=3%5Et
Then x%5E2=3%5E2t=9%5Et.
The equation turns into
3x%5E2-82x%2B27=0
Factoring, we can easily find the solutions:
3x%5E2-82x%2B27=0 --> %283x-1%29%28x-27%29=0--> system%28x=1%2F3%2C%22or%22%2Cx=27%29
Going back to t,
x=1%2F3-->3%5Et=1%2F3-->highlight%28t=-1%29
x=27-->3%5Et=27-->highlight%28t=3%29