## Natural Log Help Please: Solve ln(x) + ln(x - 1) = 1 for x

Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

### Natural Log Help Please: Solve ln(x) + ln(x - 1) = 1 for x

I am working on a problem and am stuck. I feel like my problem could be due to a lack of knowledge in arithmetic but I am not certain. The fact that there is an x^2 and an x is really 'throwing me off'.

The problem is:
Solve the equation for x.
ln(x) + ln(x - 1) = 1

The steps I took before I became stuck were as follows:
ln(x) + ln(x - 1) = 1
ln(x^2 - x) = 1 <==Log rule of addition
x^2 - x = e^1 <==Natural log simplifying
x(x - 1) = e^1 <==Factored

mrpersonality

Posts: 2
Joined: Sun Jun 27, 2010 9:22 pm

mrpersonality wrote:Solve the equation for x.
ln(x) + ln(x - 1) = 1

The steps I took before I became stuck were as follows:
ln(x) + ln(x - 1) = 1
ln(x^2 - x) = 1 <==Log rule of addition
x^2 - x = e^1 <==Natural log simplifying

Now work with the resulting quadratic equation (since "e" is just another number):

. . . . .$x^2\, -\, x\, -\, e\, =\, 0$

This can be solved with the Quadratic Formula.

stapel_eliz

Posts: 1720
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Natural Log Help Please: Solve ln(x) + ln(x - 1) = 1 for

I didn't think to use the quadratic formula. Thank you!

[1 +- sqrt(1 - 4*1*(-e))]/2
1 + sqrt(1 + 4*e)/2
2.2229
mrpersonality

Posts: 2
Joined: Sun Jun 27, 2010 9:22 pm