SOLUTION: log x + log(x+1)=2 what does x equal?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log x + log(x+1)=2 what does x equal?       Log On


   

Question 743632: log x + log(x+1)=2 what does x equal?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

log%28+x%29+%2B+log%28x%2B1%29=2

log+%28x+%29%2Flog%2810%29%2B+log%28x%2B1%29%2Flog%2810%29=2

%28log+%28x+%29%2B+log%28x%2B1%29%29%2Flog%2810%29=2

%28log%28x%28x%2B1%29%29%29%2Flog%2810%29=2

log+%28x%28x%2B1%29%29=2%2Alog%2810%29

log+%28x%28x%2B1%29%29=log%2810%5E2%29

log+%28x%28x%2B1%29%29=log%28100%29

x%28x%2B1%29=100

x%5E2%2Bx=100

x%5E2%2Bx-100=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-100%29+%29%29%2F%282%2A1%29+

x+=+%28-1+%2B-+sqrt%28+1%2B400%29+%29%29%2F2+

x+=+%28-1+%2B-+sqrt%28+401%29+%29%29%2F2+

x+=+%28-1+%2B-+20.025+%29%2F2+

solution:

x+=+%28-1+%2B+20.025+%29%2F2+
x+=+19.025%2F2+
x+=+9.5125+....since we are dealing with logarithm, we need just positive solution