Question

How do you solve `ln (4x – 2) – ln 4 = - ln (x-2)`?

Answer 1

The solution is `x=5/2`

Explanation:

We can do this like that

`ln(4x-2)-ln4=-ln(x-2)=>ln(4x-2)+ln(x-2)=ln4=>ln(4x-2)(x-2)=ln4=>(4x-2)(x-2)=4=>4x^2-8x-2x+4=4=>4x^2-10x=0=>2x(2x-5)=0=>x=0,x=5/2`

Because `x>2` the acceptable solution is `x=5/2`