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

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Answer 1 · 2015-09-10T23:08:38

The solution is $x=5/2$

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 $x=5/2$

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