SOLUTION: Please help me solve this equation. {{{lnx + ln(x+1)=2}}}. I tried bringing the foil method bringing {{{(x+1)}}} with {{{lnx}}}, but all I ended up with was {{{ln x^3=2}}} and my t

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Please help me solve this equation. {{{lnx + ln(x+1)=2}}}. I tried bringing the foil method bringing {{{(x+1)}}} with {{{lnx}}}, but all I ended up with was {{{ln x^3=2}}} and my t      Log On


   

Question 78142: Please help me solve this equation. lnx+%2B+ln%28x%2B1%29=2. I tried bringing the foil method bringing %28x%2B1%29 with lnx, but all I ended up with was ln+x%5E3=2 and my teacher said that my steps were wrong. Can you help me to find out where it is exactly I went wrong.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You cannot foil these parenthesis, you must use logarithmic identities to solve
lnx+%2B+ln%28x%2B1%29=2
ln%28x%2A%28x%2B1%29%29=2 Use the identity: ln%28x%29%2Bln%28y%29=ln%28x%2Ay%29
ln%28x%5E2%2Bx%29=2 Distribute
e%5E%28ln%28x%5E2%2Bx%29%29=e%5E2 Raise both sides to exponents with the base of e. This undoes the natural log
x%5E2%2Bx=e%5E2
x%5E2%2Bx=e%5E2 Subtract e%5E2 from both sides
x%5E2%2Bx-e%5E2=0 Since e^2 is approximately 7.3891 we can say
x%5E2%2Bx-7.3891=0
Now use the quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-7.3891+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%281%29%5E2-4%2A1%2A-7.3891=30.5564.

Discriminant d=30.5564 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+30.5564+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+30.5564+%29%29%2F2%5C1+=+2.26389218313595
x%5B2%5D+=+%28-%281%29-sqrt%28+30.5564+%29%29%2F2%5C1+=+-3.26389218313595

Quadratic expression 1x%5E2%2B1x%2B-7.3891 can be factored:
1x%5E2%2B1x%2B-7.3891+=+1%28x-2.26389218313595%29%2A%28x--3.26389218313595%29
Again, the answer is: 2.26389218313595, -3.26389218313595. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-7.3891+%29



So our answer is
x=-3.26389218313595 or x=2.26389218313595