SOLUTION: Solve: logbase4(3x^2-2x)=logbase6 36 I think the answer is {8/3}????

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve: logbase4(3x^2-2x)=logbase6 36 I think the answer is {8/3}????      Log On


   

Question 132646: Solve: logbase4(3x^2-2x)=logbase6 36 I think the answer is {8/3}????
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%283x%5E2+-+2x%29%29+=+log%286%2C36%29
log%284%2C%283x%5E2+-+2x%29%29+=+log%286%2C6%5E2%29
The right side = 2
log%284%2C%283x%5E2+-+2x%29%29+=+2
This says "The exponent to the base 4 which gives me 3x%5E2+-+2x
is 2, so
4%5E2+=+3x%5E2+-+2x
3x%5E2+-+2x+-+16+=+0
Solve using quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A3%2A%28-16%29+%29%29%2F%282%2A3%29+
x+=+%28+2+%2B-+sqrt%284+%2B+192+%29%29%2F+6+
x+=+%28+2+%2B-+14%29%2F+6+
x+=+8%2F3
x+=+-2
check answers:
log%284%2C%283x%5E2+-+2x%29%29+=+log%286%2C36%29
log%284%2C3%2A%288%2F3%29%5E2+-+2%2A%288%2F3%29%29+=+log%286%2C36%29
log%284%2C+%2864%2F3+-+16%2F3%29%29+=+2
log%284%2C+16%29+=+2
True
log%284%2C%283x%5E2+-+2x%29%29+=+log%286%2C36%29
log%284%2C%283%2A%28-2%29%5E2+-+2%2A%28-2%29%29%29+=+log%286%2C36%29
log%284%2C%2812+%2B+4%29%29%29+=+log%286%2C36%29
log%284%2C16%29+=+2
True