Question 741766
.
Solve the equation
ln(−8 − x) + ln 3 = ln(2 − x)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


<pre>
The domain to this equation is the solution set to these two inequalities

    -8 - x > 0  AND  2 - x > 0.


They define the domain as the set  { x | x < -8 }.


So, we will assume that 'x' is in this domain.


Then from the given equation, due to the properties of logarithms, we have

    (-8 - x)*3 = 2 - x,

    -24 - 3x = 2 - x

     -24 - 2 = 3x - x

        -26  =   2x

        x = -26/2 = -13.


This value -13 is in the domain, so it is the solution to the given equation.   <U>ANSWER</U>


You may <U>CHECK</U>  that at x = -13  both sides of the given equation are ln(15): 
they coincide, so the answer  is correct.
</pre>

Solved.


What is written in the post by @lynnlo is a blatant gibberish,
so ignore his/her post for the peace in your mind.