SOLUTION: Log 3 4x+log 3 (x-4) =2

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Question 1083496: Log 3 4x+log 3 (x-4) =2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%283%2C+%284x%29%29%2Blog%283%2C%28x-4%29%29+=2

log%28%284x%29%29%2Flog%28%283%29%29%2Blog%28%28x-4%29%29%2Flog%28%283%29%29+=2

%28log%28%284x%29%29%2Blog%28%28x-4%29%29%29%2Flog%28%283%29%29+=2

log%284x%28x-4%29%29%2Flog%28%283%29%29+=2

log%284x%28x-4%29%29+=2log%28%283%29%29

log%284x%28x-4%29%29+=log%28%283%5E2%29%29.......if log same, we have

4x%28x-4%29+=9

4x%5E2-16x+=9

4x%5E2-16x+-9=0

4x%5E2%2B2x-18x+-9=0

%284x%5E2%2B2x%29-%2818x+%2B9%29=0

2x%282x%2B1%29-9%282x+%2B1%29=0

%282x+-+9%29%282x+%2B+1%29+=+0
solutions:
if %282x+-+9%29+=+0->2x=9->x=9%2F2 or x=4.5
if %282x+%2B+1%29+=+0->2x=-1->x=-1%2F2 -> since log, disregard negative solution
so, your solution is: x=9%2F2 or x=4.5