SOLUTION: solve the equation and only give the exact answer. (no decimals) log(3x)+log(x-2)=log(x-4)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve the equation and only give the exact answer. (no decimals) log(3x)+log(x-2)=log(x-4)      Log On


   

Question 950730: solve the equation and only give the exact answer. (no decimals)
log(3x)+log(x-2)=log(x-4)
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
log%28%283x%29%29%2Blog%28%28x-2%29%29=log%28%28x-4%29%29

first use the addition of logs rule [loga + logb is equivalent to log(a*b)]

log%28%283x%28x-2%29%29%29=log%28%28x-4%29%29

logs on each side end up cancelling themselves out as long as everything has a log of the same base.

3x%28x-2%29=x-4
3x%5E2-6x=x-4
3x%5E2-7x%2B4=0
%283x-4%29%28x-1%29=0

3x-4=0
x=4%2F3

x-1=0
x=1

The answer is x = 1 and 4/3.