Thread: Logarithmic equation with parameter, please help

I need to find all values of the real parameter "a" for which the equation has two solutions. Find the solutions.

Hey shervlad.

Have you tried expanding out the absolute value to take care of all possible combinations?

Hint: a - log(x) + a + log(x) = 2 for a - log(x) > 0 and a + log(x) > 0 is 1 equation. Can you expand the rest and find the two common solutions?

yeah...but that's a dead-end way. What I did was I sqared the equation and so I got rid of one module, and it is much easier to work with only one module than with two, especially having to variables...
If you are interested in the solution:

You might have to re-do it since the post says your equation is too long.