SOLUTION: Log base 9 of 3 to the 3x-4=x. How do I solve for x

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Log base 9 of 3 to the 3x-4=x. How do I solve for x      Log On


   

Question 738696: Log base 9 of 3 to the 3x-4=x. How do I solve for x
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20854) About Me  (Show Source):
You can put this solution on YOUR website!
log+%289%2C%283%5E%283x-4%29%29%29=x

log+%289%2C%283%5E%283x-4%29%29%29%2Flog+%289%29=x

log+%289%2C%283%5E%283x-4%29%29%29=xlog+%289%29

log+%289%2C%283%5E%283x-4%29%29%29=log+%28%289%5Ex%29%29

log+%289%2C%283%5E%283x-4%29%29%29=log+%28%283%5E2x%29%29...if so, then

3%5E%283x-4%29=3%5E2x...if so, then

3x-4=2x........solve for x

3x-2x=4

x=4


Answer by MathTherapy(10704) About Me  (Show Source):
You can put this solution on YOUR website!
Log base 9 of 3 to the 3x-4=x. How do I solve for x

This is easier than it "looks"!!
log+%289%2C+%283%5E%283x+-+4%29%29%29+=+x
      3%5E%283x+-+4%29+=+9%5Ex ----- Converting to EXPONENTIAL form
      3%5E%283x+-+4%29+=+%283%5E2%29%5Ex
      3%5E%283x+-+4%29+=+3%5E%282x%29
        3x - 4 = 2x ----- Exponents are equated, since bases are equal
           - 4 = 2x - 3x
           - 4 = - x
         highlight%28%28-+4%29%2F%28-+1%29+=+4+=+x%29