Logarithms

Hi, for my transition work from GCSE to college I have been given some questions to do for physics regarding logarithms. Unfortunately I don't know how to use these.

There is a graph with 30.0m/s on the x axis and 50.0m/s on the y axis, with a linear line running directly proportional. The question is 'if N=N^0 e^-hg then using logarithms put it to a linear equation.' Any help please?

Reply 1

TSR Jessica

19

Sorry you've not had any responses about this. :frown:

Are you sure you’ve posted in the right place? Posting in the specific Study Help forum should help get responses. :redface:

I'm going to quote in Tank Girl now so she can move your thread to the right place if it's needed. :h:

Spoiler

Reply 2

Joinedup

20

Original post by hedgehoghog

Hi, for my transition work from GCSE to college I have been given some questions to do for physics regarding logarithms. Unfortunately I don't know how to use these.

There is a graph with 30.0m/s on the x axis and 50.0m/s on the y axis, with a linear line running directly proportional. The question is 'if N=N^0 e^-hg then using logarithms put it to a linear equation.' Any help please?

is this supposed to be a test that identifies the areas of weakness the teacher needs to help you with? if so why try beat the test, if you can't do something the teacher will realise from the test results and give you extra help.

anyway you see fomulae like N=N₀e^-Kt describing exponential decay

egs radioactive decay and the amount of charge on a capacitor while it's being discharged.

the 0 after the N is a subscript showing that it stands for the number N of things at time t=0, it's not a superscript or 'power of'

anyway the usual trick is to take natural logs

N=N₀e^-Kt
ln(N)=ln(N₀)-Kt

--

I don't understand the rest of the question about the graph.

Reply 3

username1560589

20

Original post by hedgehoghog

Hi, for my transition work from GCSE to college I have been given some questions to do for physics regarding logarithms. Unfortunately I don't know how to use these.

There is a graph with 30.0m/s on the x axis and 50.0m/s on the y axis, with a linear line running directly proportional. The question is 'if N=N^0 e^-hg then using logarithms put it to a linear equation.' Any help please?

That's strange asking you to use logs if you haven't been taught them. A log is the inverse of an exponential.
Meaning

\log_a a^n = a^{\log_a n} = n

. a is called the base and n is called the exponent
So for example if we have 100 and want to know what power of 10 that is we do

\log_{10} 100 = 2

, which you can do on your calculator using the log10 or log button. 10 is the usual base in chemistry and at this level physics too.

For manipulating logs algebraically we have the following laws(with any base that's the same across the equation):

\log a + \log b = \log ab

\log a - \log b = \log(a/b)

(

b \not{=} 0

)

\log a^n = n\log a

e is the usual base in maths and physics later on. This is because it is easier to do calculus with. e is an irrational number, like

\pi

and is roughly 2.7.

\log_e

is often written

\ln

and

\log_{10}

is often written

\log

.There should also be a ln button on your calculator.

In your example I assume you mean

N = N_0 e^{-hg}

.
If we take logs of both sides we get

\ln N = \ln (N_0e^{-hg})

.
Apply the log laws and we get a linear equation(I leave that for you).

Reply 4

hedgehoghog

OP

11

Original post by Joinedup

is this supposed to be a test that identifies the areas of weakness the teacher needs to help you with? if so why try beat the test, if you can't do something the teacher will realise from the test results and give you extra help.

anyway you see fomulae like N=N₀e^-Kt describing exponential decay

egs radioactive decay and the amount of charge on a capacitor while it's being discharged.

the 0 after the N is a subscript showing that it stands for the number N of things at time t=0, it's not a superscript or 'power of'

anyway the usual trick is to take natural logs

N=N₀e^-Kt
ln(N)=ln(N₀)-Kt

--

I don't understand the rest of the question about the graph.

Oh right thank you! It's suppose to be a test that we research the answers for that we are meant to get 100% as we are using help, but I can't find anything about this graph unfortunately! Thank you :smile:

Logarithms

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