# How do you solve # ln x + ln(x-2) = 1#?

##### 1 Answer

Jan 25, 2016

#### Explanation:

We can simplify the left hand side by using the logarithmic rule:

#ln[x(x-2)]=1#

#ln(x^2-2x)=1#

To undo the natural logarithm, exponentiate both sides with base

#e^(ln(x^2-2x))=e^1#

#x^2-2x=e#

Move the

#x^2-2x-e=0#

#x=(2+-sqrt(4+4e))/2#

Factor a

#x=(2+-2sqrt(1+e))/2#

#x=1+sqrt(1+e)#

Notice that the negative root has been taken away, since for