>>I found a solution. But I'm not sure because of your log solution.
>
>The approach is correct, but you commited a mistake.

Argggh!... :)

>This is really interesting! The function is still the logarithm to the base 10, but you managed to manipulate the functions, without using the definitions of logarithm.

Turkish students have to know these ways; there are damn exams at Turkey (High school and University). For about 1.5million students get university exam and have to pass others at that exam. Every question is one minute. There are one or two questions from every issue (for about total 100-200). You have to solve so fast so you have to know easy ways. My daughter passed high school exams she at a good high-school now and I help to prepare her pass for university exams.

You asked me ask to teacher, I just already said that to my daughter but unfortunately she said that "Teacher is giving us a lot of questions but just give solution for a few"... What a teaching... :(

A math engineer friend of mine is said about that question "This is not a teaching question, this is a selecting (candidate) question".