Question

Solve ln(x) + ln(x - 1) = 1
Please explain steps

Answer 1

Using properties of logarithims:
ln(x) + ln(x - 1) = 1
ln(x(x-1))=1
e^ln(x(x-1))=e^1
x(x-1)=e
x^2-x-e=0
Using quadratic equation x=(1+sqrt(1+4 e))/2.
Note the negative solution is not in the domain of lnx of ln(x-1) so it's not an answer