SOLUTION: I have tried to figure this equation but it doesn't come out with the right answer. Please can you help me? 9^x = 1/3sqrt 3

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I have tried to figure this equation but it doesn't come out with the right answer. Please can you help me? 9^x = 1/3sqrt 3      Log On


   

Question 130716This question is from textbook
: I have tried to figure this equation but it doesn't come out with the right answer. Please can you help me?
9^x = 1/3sqrt 3 This question is from textbook

Found 2 solutions by cngriffith, MathTherapy:
Answer by cngriffith(27) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite as (3^2)^x=1/3(3^1/2)
power to power: multiply exponents: 3^2x=1/3(3^1/2)
multiply both sides by 3: 3(3^2x)=1/3(3^1/2)(3)
like bases -add exponents 3^2x+1=3^1/2
equate exponents 2x+1=1/2
solve equation x=-1/4

Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
I have tried to  figure this equation but it doesn't come out with the right answer. Please can you help me?

9^x = 1/3sqrt 3
===============
It would've been NICE if you'd posted your work! Then, one would've been able to point out your error(s), or
you may've been able to identify it/them, yourself.
   9%5Ex+=+%281%2F3%29sqrt%283%29
matrix%282%2C1%2C+%22+%22%2C+%283%5E2%29%5Ex+=+%283%5E%28-+1%29%29%283%5E%281%2F2%29%29%29 ----- Converting all expressions to base 3
matrix%282%2C1%2C+%22+%22%2C+3%5E%282x%29+=+3%5E%28%28-+1+%2B+1%2F2%29%29%29
matrix%282%2C1%2C+%22+%22%2C+3%5E%282x%29+=+3%5E%28-+1%2F2%29%29
  2x+=+-+1%2F2 ---- EQUATING exponents, since bases are equal
   4x = - 1 --- Cross-multiplying  
   highlight%28x+=+-+1%2F4%29