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How do I find what t is?
Does anyone mind explaining how to do it? I haven't done it in maths yet.
Thanks.
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the operation your looking for is the logarithm - in this case the natural logarithm (logarithm base e)
logarithm is the inverse operation of exponential. i.e.
for example:
i say in the reals, because in the complex numbers, logarithm is non unique, but you can be assured that for all real x and a this will hold
so in otherwords:
you can work out the right hand side on a calculator, and then divide by the coefficient of 't' to get the value of 't'
note that
going from original equation:
Last edited by luca-deltodesco (2007-10-08 09:07:46)
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Aah right, not too difficult.
Thanks luca
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also, realise that working it out using my last formula in terms of N and lambda will give more accurate results when computed using either a computer or a calculator as you are dealing with large numbers instead of very small numbers, and logarithm's are better approximated with large rather than small numbers.
working it out with your rearrangement i get:
2738274191766.0933
which when plugged into first equation will give a difference in values of :
1620000000
whereas using direct rearrangement for t in terms of N and lambda with two logarithms gives
2738396562095.8906
which gives a difference of:
0.0029296875
very different results, but you can see that either would give you a right answer in any question since they aern't going to ask for accuracy beyond 4 significant figures
in other notes, wow thats a long half life, over 86 thousand years o.O
Last edited by luca-deltodesco (2007-10-08 09:17:54)
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