SOLUTION: How would I solve for x? log(x)+log(x+15)=2 I can only get it to: log[x(x+15)]=2, is that even right? What should I do next?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How would I solve for x? log(x)+log(x+15)=2 I can only get it to: log[x(x+15)]=2, is that even right? What should I do next?       Log On


   

Question 29882: How would I solve for x?
log(x)+log(x+15)=2
I can only get it to: log[x(x+15)]=2, is that even right? What should I do next?
Found 2 solutions by Paul, josmiceli:
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Your first step is correct:
log[x(x+15)]=2
simplfy this
logx%5E2%2B15x=2
Apply base of 10 with the power of 2
x%5E2%2B15x=10%5E2
x%5E2%2B15x-100=0
a=, b=15, c=-100
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=%28-15%2B-sqrt%2815%5E2-4%2A1%2A-100%29%29%2F%282%2A1%29
Simplfy you get two solutions
x=-20 and x=5
Remove the negative.

Hence, the solution to the logarith equation is 5.
Paul.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
log(x)+log(x+15)=2
log(x(x+15)) = 2
log(x^2 +15x) = 2
assume log is to the base 10
10^2 = x^2 + 15x
x^2 +15x -100 = 0
(x + 20)(x - 5) = 0
x = -20
x = +5
check
log(-20)+log(-20+15)=2
log( (-20)(-5)) = 2
log(100) = 2
10^2 = 100
checks
and
log(x)+log(x+15)=2
log(5(5+15)) = 2
log(100) = 2
10^2 = 100
checks