SOLUTION: How would I solve this problem, I have tried but cannot figure it out: Solve. Be sure to reject any value of x that is not in the domain of the original equation. {{{ log (3,

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How would I solve this problem, I have tried but cannot figure it out: Solve. Be sure to reject any value of x that is not in the domain of the original equation. {{{ log (3,      Log On


   

Question 981321: How would I solve this problem, I have tried but cannot figure it out:
Solve. Be sure to reject any value of x that is not in the domain of the original equation.
+log+%283%2C+%28+x+-+5+%29%29+%2B+log+%283%2C+%28+x+%2B+3+%29%29+=+2+
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

+log+%283%2C+%28+x+-+5+%29%29+%2B+log+%283%2C+%28+x+%2B+3+%29%29+=+2+

+log+%283%2C+%28%28+x+-+5+%29+%28+x+%2B+3+%29%29%29+=+2+....change the base

+log+%28+%28%28+x+-+5+%29+%28+x+%2B+3+%29%29%29%2Flog+%283%29+=+2+

+log+%28+%28%28+x+-+5+%29+%28+x+%2B+3+%29%29%29=+2log+%283%29++

+log+%28+%28%28+x+-+5+%29+%28+x+%2B+3+%29%29%29=+log+%283%5E2%29++

+log+%28+%28%28+x+-+5+%29+%28+x+%2B+3+%29%29%29=+log+%289%29++.....if log same, then

+%28+x+-+5+%29+%28+x+%2B+3+%29=+9++....solve for x

++x%5E2%2B3x+-+5x+-15=+9++

++x%5E2+-+2x+-15-9+=0++

++x%5E2+-+2x+-24+=0++....factor completely, write -2x as 4x-6x

++x%5E2%2B4x+-+6x+-24+=0++......group

++%28x%5E2%2B4x+%29-+%286x+%2B24%29+=0++

++x%28x%2B4+%29-+6%28x+%2B4%29+=0++

%28x-6%29%28x%2B4%29+=+0

solutions:
if %28x-6%29+=+0=>x=6
if %28x%2B4%29+=+0=>x=-4....disregard negative solution because
the domain of the original equation is { x element R : x%3E5 }

so,your solution is =>x=6