SOLUTION: Hi and thanks for the help! I was wondering how to solve log base square root 3 to the 1/9=x. also one other question is to change the exponential equation to a log... x^3=729

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Hi and thanks for the help! I was wondering how to solve log base square root 3 to the 1/9=x. also one other question is to change the exponential equation to a log... x^3=729       Log On


   

Question 871834: Hi and thanks for the help! I was wondering how to solve log base square root 3 to the 1/9=x. also one other question is to change the exponential equation to a log... x^3=729
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39720) About Me  (Show Source):
You can put this solution on YOUR website!
Your first one is either incomplete or wrong.

Your second one is solvable.
x%5E3=729
x%5E3=9%2A9%2A9---see, the base is 9.
log%28x%2C729%29=3

Answer by MathTherapy(10699) About Me  (Show Source):
You can put this solution on YOUR website!
Hi and thanks for the help! I was wondering how to solve log base square root 3 to the 1/9=x. also one other question is
to change the exponential equation to a log... x^3=729 

If log+%28sqrt%283%29%2C+%281%2F9%29%29+=+x, then:
       %28sqrt%283%29%29%5Ex+=+1%2F9+ ---- Converting to EXPONENTIAL form
   matrix%282%2C1%2C+%22+%22%2C+%283%5E%281%2F2%29%29%5Ex%29+=+1%2F9 ---- Converting sqrt%283%29 to matrix%282%2C1%2C+%22+%22%2C+3%5E%281%2F2%29%29
       matrix%282%2C1%2C+%22%22%2C+3%5E%28x%2F2%29%29+=+1%2F9
      matrix%281%2C2%2C+matrix%282%2C1%2C+%22+%22%2C+3%5E%28x%2F2%29%29%2C+%22=%22%29%29matrix%282%2C1%2C+%22+%22%2C+3%5E%28++-++2%29%29
          x%2F2+=++-++2 ----- Bases are equal, and so are the exponents
          x = 2(- 2) = - 4