C4 maths how does ln K equal A?

The questions are like ln K and then the mark scheme they turn ln K into Ae something, how are they turning the ln K into A??

Reply 1

Kevin De Bruyne

Original post by Rosalie_aqua

The questions are like ln K and then the mark scheme they turn ln K into Ae something, how are they turning the ln K into A??

It's not 100% clear what you're asking (perhaps a link to a question would be useful).

But if you integrated something to give ln(f(x)) + c, where f is some function of x for example and c is the constant of integration, then you can say that c = lnA (which is general, but some examples are like if c = 2, then A = e^2 so lnA = lne^2 = 2lne = 2).for some A value, and then use that log(a) + log(b) = log(ab) to give you ln(Af(x)).

(edited 7 years ago)

Reply 2

electrifeye

k and A are both arbitrary constants, for example if I integrated to find that y = 5x + C, I could also say that 2y = 10x + A, where A = 2C. It's often easier to get a new constant each time than work with multiples of C or k all the time.

The same principle applies to using e and ln. If I have y = e^k, then as e^k is constant I can say that y = A, where A = e^k. Likewise if I can say that e^(x+2) = (e^2)(e^x) = Ae^x

It's just a way of tidying up your answers to make them a bit simpler. It's important to note that unless it's a show that you probably wouldn't lose marks for not doing this, but I would still learn it as it keeps your solutions tidy and keeps you on the safe side if the examiners are picky about it. If you don't understand or want me to go over something in more detail feel free to ask :smile: