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

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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(20063)   (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)   (Show Source): You can put this solution on YOUR website!
Solve for x over the real numbers:

Move everything to the left hand side.
Subtract log(5)+log(x-2) from both sides:

Combine logarithms.

Eliminate the logarithm from the left hand side.
Cancel logarithms by taking exp of both sides:

Multiply both sides by a polynomial to clear fractions.
Multiply both sides by 5 (x-2):

Write the linear polynomial on the right hand side in standard form.
Expand out terms of the right hand side:

Isolate x to the left hand side.
Subtract 5 x from both sides:

Solve for x.
Divide both sides by -2:
Answer:
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