Question 954792
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Solve log2(x-2)-log2(x+5)=3
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The solution, x = - 6, by the other person who responded, is WRONG!! 

{{{log (2, (x - 2)) - log (2, (x + 5)) = 3}}}
The SMALLER of the 2 log arguments, x - 2 MUST be > 0. So, x - 2 > 0 ===> x > 2.
We then have: {{{log (2, (x - 2)) - log (2, (x + 5)) = 3}}}, with x > 2.
                                           {{{log (2, ((x - 2)/(x + 5))) = 3}}} ----- Applying {{{log (b, (c)) - log (b, d))}}} = {{{log (b, (c/d))}}}
                                                       {{{(x - 2)/(x + 5) = 2^3}}} ---- Converting to EXPONENTIAL form 
                                                       {{{(x - 2)/(x + 5) = 8}}}
                                                   8(x + 5) = x - 2 ----- Cross-multiplying 
                                                    8x + 40 = x - 2 
                                                        8x - x = - 2 - 40
                                                              7x = - 42                                                                                                 
                                                                {{{x = (- 42)/7 = - 6}}} 
                                              
The x-value, - 6, is NOT > 2, and is therefore an EXTRANEOUS solution, which makes it an INVALID/UNACCEPTABLE solution. 
So, this equation DOESN'T have a solution!!</font></font></font></b></pre>