# Homework Help: Solving a logarithmic equation.

1. Oct 26, 2012

### thatguythere

1. The problem statement, all variables and given/known data
log3x+log3(2x+1)=1
Solve for x.

2. Relevant equations

3. The attempt at a solution
log3((2x+1)x)=1
3log3((2x+1))=31
(2x+1)x=3
2x2+x=3
2x2+x-3=0

x= (-1±√(12-4(2)(-3)))/(2(2))
= (-1±√(1+24))/(4)
= (-1±√25)/(4)
= (-1±5)/(4)
= 4/4 or -6/4

Is there no solution?

2. Oct 26, 2012

### SteamKing

Staff Emeritus
What's wrong with the two solutions you got from solving the quadratic eqn.?

3. Oct 26, 2012

### thatguythere

Logarithms with negative values are undefined though aren't they? So only 4/4 or 1 would be correct?

4. Oct 26, 2012

### Staff: Mentor

You should simplify answers such as these. You have x = 1 or x = -3/2. There is still some work to do, though.

5. Oct 26, 2012

### SammyS

Staff Emeritus
Yes, the other answer is what's called an extraneous solution.

6. Oct 26, 2012

### thatguythere

If I have x =1 and x =-3/2 and I know that -3/2 is an extraneous answer, then x = 1. I am not certain what else there is to do.

7. Oct 27, 2012

### Staff: Mentor

If you've checked your solution and it works, you're done.