How do you solve ## ln (x – 2) + ln (x + 2) = ln 5##?

x=-3 or x=3

Using the property that says :

## ln(a) +ln(b) = ln(a*b)## We have:

##ln(x-2)+ln(x+2) = ln5##

##ln((x-2)*(x+2)) = ln5##

Rasing exponential both sides we will have:

##(x-2)*(x+2) =5 ##

Applying polynomial property on the equation above that says:

## a^2 - b^2 = (a-b)*(a+b)##

We have: ##(x-2)*(x+2) = x^2-4##

So, ##x^2 - 4 = 5 ## ##x^2 - 4 -5 =0## ##x^2 - 9 =0## ##(x-3)*(x+3)=0##

So, ##x-3=0## thus ##x=3##

Or,

##x+3=0## thus ##x=-3##