SOLUTION: solve for x: 1+log2(x^2-4x-16)=log2(x^2-3x+4)

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Question 1198977: solve for x: 1+log2(x^2-4x-16)=log2(x^2-3x+4)
Found 3 solutions by MathLover1, greenestamps, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

solve for x:
1%2Blog%282%2Cx%5E2-4x-16%29=log%282%2Cx%5E2-3x%2B4%29
1=log%282%2Cx%5E2-3x%2B4%29-log%282%2Cx%5E2-4x-16%29
1=log%282%2C%28x%5E2-3x%2B4%29%2F%28x%5E2-4x-16%29%29..........log%282%2C2%29=1
log%282%2C2%29=log%282%2C%28x%5E2-3x%2B4%29%2F%28x%5E2-4x-16%29%29
2=%28x%5E2-3x%2B4%29%2F%28x%5E2-4x-16%29
2%28x%5E2-4x-16%29=%28x%5E2-3x%2B4%29
2x%5E2-8x-32=x%5E2-3x%2B4
2x%5E2-8x-32-x%5E2%2B3x-4=0
x%5E2-5x-36=0..........use quadratic formula
x=%28-%28-5%29%2B-sqrt%28%28-5%29%5E2-4%2A1%2A%28-36%29%29%29%2F%282%2A1%29
x=%285%2B-sqrt%2825%2B144%29%29%2F2
x=%285%2B-sqrt%28169%29%29%2F2
x=%285%2B-13%29%2F2
solutions:
x=%285%2B13%29%2F2=>x=9
x=%285-13%29%2F2=>x=-4

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


1%2Blog%282%2C%28x%5E2-4x-16%29%29=log%282%2C%28x%5E2-3x%2B4%29%29

Rewrite the first term on the left as a base 2 logarithm.

log%282%2C%282%29%29%2Blog%282%2C%28x%5E2-4x-16%29%29=log%282%2C%28x%5E2-3x%2B4%29%29

Use the rule for adding logarithms with the same base.

log%282%2C%282%28x%5E2-4x-16%29%29%29=log%282%2C%28x%5E2-3x%2B4%29%29

log%282%2C%282x%5E2-8x-32%29%29=log%282%2C%28x%5E2-3x%2B4%29%29

Set the arguments equal to each other and solve the resulting quadratic equation.

2x%5E2-8x-32=x%5E2-3x%2B4
x%5E2-5x-36=0
%28x-9%29%28x%2B4%29=0
x=9 or x=-4

Both values satisfy the original equation, so

ANSWERS: x = 9 or x = -4

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

solve for x: 1+log2(x^2-4x-16)=log2(x^2-3x+4)
You DON'T need to use the quadratic equation formula to solve this, as that woman did!


                   ----- Applying 
                   ----- Applying 
                matrix%281%2C3%2C+2%28x%5E2+-+4x+-+16%29%2C+%22=%22%2C+x%5E2+-+3x+%2B+4%29 ----- Cross-multiplying
        
                (x - 9)(x + 4) = 0
                         x - 9 = 0     or      x + 4 = 0