SOLUTION: solve log(x+20)-log(x+2)=logx

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: solve log(x+20)-log(x+2)=logx      Log On


   

Question 615686: solve log(x+20)-log(x+2)=logx
Found 2 solutions by math33, MathTherapy:
Answer by math33(31) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
solve log(x+20)-log(x+2)=logx

log (x + 20) - log (x + 2) = log x

log %28%28x+%2B+20%29%2F%28x+%2B+2%29%29 = log %28x%29

%28x+%2B+20%29%2F%28x+%2B+2%29+=+x

x(x + 2) = x + 20 ----- Cross-multiplying

x%5E2+%2B+2x+=+x+%2B+20

x%5E2+%2B+2x+-+x+-+20+=+0

x%5E2+%2B+x+-+20+=+0

(x + 5)(x - 4) = 0

x + 5 = 0 or x - 4 = 0

x = - 5 (EXTRANEOUS) or x = highlight_green%284%29

=======
Check
=======
log (x + 20) - log (x + 2) = log x

log (4 + 20) - log (4 + 2) = log 4 ------ Substituting 4 for x in original equation

log (24) - log (6) = log 4

log %2824%29%2F6 = log 4

log (4) = log 4 (TRUE)

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com