SOLUTION: Find x. {{{log3 (x + 1) + log3 (x - 5) = 3}}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find x. {{{log3 (x + 1) + log3 (x - 5) = 3}}}       Log On


   

Question 267189: Find x.
log3+%28x+%2B+1%29+%2B+log3+%28x+-+5%29+=+3
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
log3+%28x+%2B+1%29+%2B+log3+%28x+-+5%29+=+3
Adding logs is the same as multiply
log3%28%28x+%2B+1%29%2A%28x+-+5%29%29+=+3
FOIL
log3%28x%5E2+-+5x+%2B+x+-+5%29+=+3
:
log3%28x%5E2+-+4x+-+5%29+=+3
The exponent equiv of logs
x%5E2+-+4x+-+5+=+3%5E3
:
x^2 - 4x - 5 = 27
:
x^2 - 4x - 5 - 27 = 0
:
x^2 - 4x - 32 = 0
Factor
(x-8)(x+4) = 0
positive solution (cannot have a log of a neg number)
x = 8
:
See if this works
log3+%289%29+%2B+log3+%283%29+=+3
log3+%2827%29+=+3
Exponent equiv:
27 = 3^3