SOLUTION: Solve: 2log(base4)x+log(base4)3=log(base4)x-log(base4)2

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Question 240559: Solve: 2log(base4)x+log(base4)3=log(base4)x-log(base4)2
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
2%2Alog%284%2Cx%29%2Blog%284%2C3%29=log%284%2Cx%29-log%284%2C2%29

log%284%2Cx%5E2%29%2Blog%284%2C3%29=log%284%2Cx%29-log%284%2C2%29
log%284%2C3x%5E2%29=log%284%2Cx%2F2%29
3x%5E2=x%2F2

Multiply both sides by 2:
6x%5E2+=x
6x%5E2-x=0

Factor the x:
x%286x-1%29=0
There are two solutions:
x=0 NOTE: THIS ANSWER MUST BE REJECTED, SINCE log(0) is UNDEFINED!!

6x-1=0
6x=1
x=1/6 This one seems to work!!

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus