- #1

- 36

- 3

I just can get it

This problem has been driving me crazy for a week now

[tex]If\quad a,b,c\quad \neq \quad 1\\ Also\quad (log_{ b }{ a\cdot }log_{ c }{ a }\quad +\quad log_{ a }{ a })\quad +\quad (log_{ a }{ b\cdot }log_{ c }{ b }\quad +\quad log_{ b }{ b })\quad +\quad (log_{ a }{ c\cdot }log_{ b }{ c }\quad +\quad log_{ c }{ c })\quad =\quad 0\\ Prove\quad that\quad \\ abc\quad =\quad 1\\ Additionally\\ If\quad a,b,c\quad =\quad 1\quad Prove\quad a=b=c[/tex]

My attempt

So what I did was

call log_a b = p ,log_b = q,log_c a=q

I plugged this in and made an interesting discovery

pqr = 1

So i used this in the equation above and tried to get to the proof but didn't work

Where am I faltering

?