## anonymous one year ago Hi everyone : hope ur well so I have this log plus absolute question so. For ln (x-2) = ln (2-x) I know there is no solution however for ln |x-2| = ln |2-x| There is , someone can kindly how is that possible and also help me solve this thank u

1. Nnesha

how did you get *no solution* ???

2. anonymous

For the first one

3. anonymous

.

4. alekos

i would imagine that there is a solution

5. anonymous

Well when u do the inequality of x-2 and 2-x it states that x is bigger than two but at the same time less than two but in reality that's not possible thus no solution

6. anonymous

However for absolute the answer is always positive

7. Nnesha

$\huge\rm\cancel{ ln} (x-2) = \cancel{\ln}(2-x)$ x-2 =2-x isn't it right ?

8. anonymous

Nope u have to check their inequality first then check if their 1-1 function then u can do the step u did

9. Nnesha

0_o okay? o_0 i should leave... ;P

10. anonymous

@ganeshie8 can u plz help me

11. anonymous

@Abhisar

12. alekos

If you plot a graph of both functions you will see that as x approaches 2 then y tends to +inf so there really is no valid solution except to say that $\lim_{x \rightarrow 2} \ln \left| x-2 \right| = \lim_{x \rightarrow 2} \ln \left| 2-x \right|$

13. Nnesha

0_o lim .-. i'm sorry @ayeshaafzal221 _-_