SOLUTION: ln(−8 − x) + ln 3 = ln(2 − x)

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Question 741763: ln(−8 − x) + ln 3 = ln(2 − x)
Found 2 solutions by lynnlo, ikleyn:
Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
-10 ln + ln^3=0

Answer by ikleyn(53427) About Me  (Show Source):
You can put this solution on YOUR website!
.
Solve the equation
ln(−8 − x) + ln 3 = ln(2 − x)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

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.   ANSWER


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

Solved.

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