Logarithms????

I do chemistry ocr A level, and I have to something about logs. I have no idea what a "Log" is and I dont know what an "e" is, but we use them when we do half life? Can someone explain what ln2/k means? I tried asking my chemistry teacher and people who do maths but it seems like nobody really knows
If someone could explain this concept in REALLY simple words that would be so helpful

e is just a (irrational) constant like pi. Its value is about 2.7 and it may seem a bit strange but its a closely associated with calculus and hence stuff like half lives etc. So we can talk about powers of e
e^2 ~ 7.4
e^(-1) ~ 0.37
e^(-2) ~ 0.135
etc ....
Logs are functions which allow you to do arithmetic on the exponents/powers so the 2,-1,-2 in the previous examples.
You have radioactive decay curves which are described by exponential decay
https://en.wikipedia.org/wiki/Exponential_decay
n(t) = N_0 e^(-kt)
and you can get the time taken to decay to half the initial value by doing a bit of rearrangement and using logs as in
https://www.savemyexams.com/a-level/physics/aqa/17/revision-notes/8-nuclear-physics/8-2-radioactive-decay/8-2-3-half-life/
which is your ln(2)/k. Everytime the time increases by ln(2)/k, your activity halves which is the property of an exponential curve/function.
I guess the key thing is to understand exponential curves and exponential decay and not be put off by "e" which is just a constant wtih value about 2.7.

Im sorry but this doesnt make sense to me, what is "n(t) - N_0" or whatever, and what is the "2,-1,-2." I dont do physics or maths so it doesnt make any sense to me 😭

If youre doing about logs, half life, ... what is it in the context of? For gcse maths you should have come across exponential curves and exponential decay? Similarly in physics gcse you should have done radioactive decay?

I'm doing half life in chemistry a level, all I know about radioactive decay is that unstable nucleus releases energy, but that doesn't have to do with what I'm studying, And I've never heard of exponential decay before. I only know that exponential curves are the curves are go up or down rapidly. We never mentioned any of these things in class, I've only seen certain equations like k = ln2/t1/2 when finding half life of a first order reaction and the Arrhenius equation,

From bbc bitesize (gcse)
Exponential functions https://www.bbc.co.uk/bitesize/guides/zc62srd/revision/4
Half life (radioactive decay) https://www.bbc.co.uk/bitesize/guides/zxbnh39/revision/3
So you should have covered some of the ideas at gcse.
In reaction kinetics
https://pmt.physicsandmathstutor.com/download/Chemistry/A-level/Notes/CIE/A2-Physical-Chemistry/Detailed/8.%20Reaction%20Kinetics.pdf
The concentration that youre interested in (first order ...) is an exponential decay so the concentration at time t, c(t), is given by
c(t) = C_0 e^(-kt)
where C_0 is the inital concentration. k scales/mutliplies time and determines how fast or slow the reaction happens. The half life, T, is determined by the time to get to
c(T) = C_0 / 2.
and you use logs to get an expression for T. The ln(2) is because of the /2, and the k divisor is because of the time mulitplier.
So you really need to be happy with the exponential decay curve that is used to describe how the reaction concentration varies (decays) with time. You also need to be happy with what a half life represents, so the time take to halve the concentration. Then the log function is used to link the two bits together to get an expression for the half life T in terms of the reaction rate parameter k.

Thanks, but I dont think we use exponential decay curve in half life and orders of reactions in any of our classes or specification💔

logs are used to find the power of something. for eg 2^x = 8, you could just enter log₂ 8 in your calculator to find x.

That makes sense actually! thanks!!😄

From bbc bitesize (gcse)
Exponential functions https://www.bbc.co.uk/bitesize/guides/zc62srd/revision/4
Half life (radioactive decay) https://www.bbc.co.uk/bitesize/guides/zxbnh39/revision/3
So you should have covered the two main ideas at gcse.
In reaction kinetics
https://pmt.physicsandmathstutor.com/download/Chemistry/A-level/Notes/CIE/A2-Physical-Chemistry/Detailed/8.%20Reaction%20Kinetics.pdf
The concentration that youre interested in (first order ...) is an exponential decay so the concentration at time t, c(t), is given by
c(t) = C_0 e^(-kt)
where C_0 is the inital concentration. k scales/mutliplies time and determines how fast or slow the reaction happens. The half life, T, is determined by the time to get to
c(T) = C_0 / 2.
and you use logs to get an expression for T. The ln(2) is because of the /2, and the k divisor is because of the time mulitplier.
So you really need to be happy with the exponential decay curve that is used to describe how the reaction concentration varies (decays) with time. You also need to be happy with what a half life represents, so the time take to halve the concentration. Then the log function is used to link the two bits together to get an expression for the half life T in terms of the reaction rate parameter k.