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# Logarithm Questions watch

1. I've put this on a word document cos its easier to do all the powers etc. than on here.

Please would someone explain to me the working of these two questions.
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2. logarithm question.doc (19.0 KB, 199 views)
3. (Original post by Jessie)
I've put this on a word document cos its easier to do all the powers etc. than on here.

Please would someone explain to me the working of these two questions.
for first one, divide both sides by 4 (i.e. move 4 across), so you get e^2x = 1.995.
then take 'ln' of both sides, so you get 2x = ln(1.995)
so x = 0.5ln(1.995)
4. Thank you very much Mockel...I couldn't find it anywhere in my P2 textbook, although im sure its there.
5. N = c(1 - e^-kt)

=>N/c = 1 - e^-kt

=> e^-kt = 1 - N/c

=> ln (e^-kt) = ln (1 - N/c)

=> -kt = ln (1 - N/c)

=> t = -(1/k)ln(1 - N/c)

=> t = (1/k)ln [(1 - N/c)^-1]

=> t = (1/k)ln [1/(1 - N/c)]

=> t = (1/k)ln [c/(c - N)]
6. second one:
take 'c' across, and rearranging you should get:

e^(-kt) = 1 - (N/c)

making it a single fraction:

e^(-kt) = (c-N) / c

'ln' both sides:

-kt = ln[ (c-n) / c]

t = (-1/k).ln[ (c-n) / c]

multiplying the '-' inside the 'ln' will cause it to 'flip':

t = (1/k).ln[ c / (c-n)]
7. Thank you very much...I'll have a look at that and try and get my head round it.

Probably easier once i've written it out neatly and with all the powers done properly.

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