SOLUTION: simplify the expression 3 log 3 (6x-4) I don't know how to write like the paper shows. log is like an exponent and the second 3 is lower than the first 3. The (6x-4) is writt

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: simplify the expression 3 log 3 (6x-4) I don't know how to write like the paper shows. log is like an exponent and the second 3 is lower than the first 3. The (6x-4) is writt      Log On


   

Question 464665: simplify the expression
3 log 3 (6x-4)
I don't know how to write like the paper shows. log is like an exponent and the second 3 is lower than the first 3. The (6x-4) is written like an exponent.
Thanks
Chris
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
If it's supposed to be written this way:
3%5E%28log%283%2C%286x-4%29%29%29,
then the answer is simply
6x-4.
This answer springs from the fact that the logarithmic function f%28x%29+=+a%5Ex has inverse function f%5E%28-1%29%28x%29+=+log%28a%2C+x%29. Then from algebra we know that
x+=+f%28f%5E%28-1%29%28x%29%29+=+a%5Elog%28a%2Cx%29.
(Notes: 1) a > 0 and a%3C%3E1
2) Both functions f%28x%29+=+a%5Ex and f%5E%28-1%29%28x%29+=+log%28a%2C+x%29 are 1-to-1, and hence have inverses.)