SOLUTION: Dear Tutor thank you for sloving this question in advance How do you slove this equation and find x 1+ 2lg(x+1)= lg(2x+1)+lg(5x+8)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Dear Tutor thank you for sloving this question in advance How do you slove this equation and find x 1+ 2lg(x+1)= lg(2x+1)+lg(5x+8)      Log On


   

Question 107587: Dear Tutor thank you for sloving this question in advance
How do you slove this equation and find x
1+ 2lg(x+1)= lg(2x+1)+lg(5x+8)
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
1%2B+2log%28x%2B1%29=+log%282x%2B1%29%2Blog%285x%2B8%29

SInce log%2810%29=1,
log%2810%29+%2B+2log%28x%2B1%29=+log%282x%2B1%29%2Blog%285x%2B8%29
and,

And, log%28xy%29=log%28x%29+%2Blog%28y%29. So,
log%2810%28x%2B1%29%5E2%29=log%28%282x%2B1%29%285x%2B8%29%29

Also, if log+x=log+y, then, x=y. Using this,
10%28x%2B1%29%5E2=%282x%2B1%29%285x%2B8%29
10%28x%2B1%29%28x%2B1%29=%282x%2B1%29%285x%2B8%29
10%28x%28x%2B1%29%2B1%28x%2B1%29%29=2x%285x%2B8%29%2B1%282x%2B8%29
10%28%28x%5E2%2Bx%29%2B%28x%2B1%29%29=%2810x%5E2%2B16x%29%2B%282x%2B8%29
10%28x%5E2%2B%28x%2Bx%29%2B1%29=10x%5E2%2B%2816x%2B2x%29%2B8
10%28x%5E2%2B2x%2B1%29=10x%5E2%2B18x%2B8
10x%5E2%2B20x%2B10=10x%5E2%2B18x%2B8
10x%5E2-10x%5E2%2B20x%2B10=10x%5E2-10x%5E2%2B18x%2B8
0%2B20x%2B10=0%2B18x%2B8
20x%2B10=18x%2B8
20x-18x%2B10=18x-18x%2B8
2x%2B10=0%2B8
2x%2B10=8
2x%2B10-10=8-10
2x%2B0=-2
2x=-2
2x/2=-2/2
x=-1

Power up,
HyperBrain!