Please explain this simple rule of logarithms to me Right I know this one is simple and I know that I just need a push to make it sink in in my head..
I am studying control systems and in one of the tutorial examples the tutor says 
Show that
$$20\log(1/x) = -20\log(x)$$
I know that when you have a divide or a multiply with logarithms you add them and subtract them but for my own understanding I just need someone to like slowly show me how this works..
If I take the log of the numerator I have $20\log(1) = 0$ but I don't know where to go from here.. So do I now just take the log of the denominator and as the numerator was zero it is just minus whatever the log of the denominator is... Getting myself a bit muddled.. Thanks

You have : $0 = 20\times\log(1) = 20\times\log(x\times\frac1{x})$
But $\log(x\times \frac1{x})=\log(x)+\log(\frac1{x})$.
So $0=20(\log(x)+\log(\frac1{x}))$ and you have your result.
