[IMG]file:///C:/DOCUME%7E1/ADMINI%7E1/LOCALS%7E1/Temp/moz-screenshot.png[/IMG]Can you help for the functions and prove at the attachment ?
The key is to show that and for some constants .
Now logrithm is not such a scary beast. Personally, I remember only three properties of logarithms.
(1) Definition: iff
(2)
(3) .
It's not difficult to deduce (2) and (3) from (1), so the main thing you need to remember is that logarithm is an inverse function to power: and .
So, how to express through ? Let . By (1), . We need to use , so let's take of both sides: . By (2), . Recalling the definition of , we get .
It's also easy to remember this last formula. Here is a mnemonic (not mathematical) explanation: you go from to ( ), then from to ( ) and the result is from to ( ).