Question

How do you solve `ln(x-1) = ln6-ln x`?

Answer 1

`x=3`

Explanation:

As `ln(x-1)=ln6-lnx`, the domain of `x` is given by `x-1>0` i.e. `x>1`.

As we have `ln(x-1)=ln6-lnx`

or `ln(x-1)=ln(6/x)`

or `x-1=6/x`

or `x^2-x=6`

or `x^2-x-6=0`

or `x^2-3x+2x-6=0`

or `(x-3)(x+2)=0`

i.e. `x=3` or `x=-2`

But as `-2` is not domain,

Solution is `x=3`