SOLUTION: log 3x = log 5 + log (x - 2) I think I am getting this. But when I follow the equation, my answer is just off, not sure where I'm going wrong now. Can some one please help, sh

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log 3x = log 5 + log (x - 2) I think I am getting this. But when I follow the equation, my answer is just off, not sure where I'm going wrong now. Can some one please help, sh      Log On


   

Question 828281: log 3x = log 5 + log (x - 2)
I think I am getting this. But when I follow the equation, my answer is just off, not sure where I'm going wrong now. Can some one please help, show me the error of my ways.
thanks
Found 2 solutions by Edwin McCravy, kmadison:
Answer by Edwin McCravy(20062) About Me  (Show Source):
You can put this solution on YOUR website!
log(3x) = log(5) + log(x-2)

Use this rule on the right:

Taking out log of an addition changes the
addition to multiplication:

log(3x) = log[5(x-2)]

log(3x) = log[5x-10]

Use the rule:   if log(A)=log(B) then A=B

     3x = 5x-10
    
    -2x = -10

      x = 5

Edwin

Answer by kmadison(20) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x over the real numbers:
log%283+x%29+=+log%285%29%2Blog%28x-2%29
Move everything to the left hand side.
Subtract log(5)+log(x-2) from both sides:
-log%285%29-log%28x-2%29%2Blog%283+x%29+=+0
Combine logarithms.

Eliminate the logarithm from the left hand side.
Cancel logarithms by taking exp of both sides:
%283+x%29%2F%285+%28x-2%29%29+=+1
Multiply both sides by a polynomial to clear fractions.
Multiply both sides by 5 (x-2):
3+x+=+5+%28x-2%29
Write the linear polynomial on the right hand side in standard form.
Expand out terms of the right hand side:
3+x+=+5+x-10
Isolate x to the left hand side.
Subtract 5 x from both sides:
-2+x+=+-10
Solve for x.
Divide both sides by -2:
Answer: x+=+5