Please explain this simple rule of logarithms to me
Right I know this one is simple and I know that
Keenan Santos
Answered question
2022-07-06
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
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 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
Answer & Explanation
Caiden Barrett
Beginner2022-07-07Added 20 answers
First of all, forget the in front, all you have to do is see that
You accept the fact that
and use the fact that , giving you
You use the fact that
and that , giving you
You use the fact that , that and that
giving you
From the equation
you get
Note that all these derivations can be transformed into each other and are equivalent. I am presenting them all because everybody looks to logarighms in his own way, so make your pick of the favorite.
Grimanijd
Beginner2022-07-08Added 4 answers
Essential for logarithms is equality
This under the conditions , and Asking: 'to what power must () be raised to get () as outcome?' is the same thing as asking: 'what is the logarithm of on base of ?' The answer is clearly . We have and equivalent is the expression: Note that:
so the fact that tells us that is raised in these cases to the same power. Our conclusion is:
Every rule concerning logarithms can derived likewise. For instance: