Question

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

Answer 1

`x = (1 + sqrt (1 + 4 e ))/2=2.22287`, nearly.

Explanation:

`x > 1` to make both `ln x and ln (x - 1 )` real.

ln x + ln ( x - 1 ) = ln (x(x-1)) = 1 = ln e#.

So, `x(x-1) = e`. Solving,

`x .=.(1+-sqrt(1+4e))/2`

Negative root is inadmissible.

The positive root is 2,22287, nearly .