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finding limiting magnitude of telescope 8 inches

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finding limiting magnitude of a star

L(8) =8.8 +5.1 log 8  the answer in the book is 13.4 but I can't figure how they got that

Mar 26th, 2015

Hi dcon,

So perhaps it's clearer if they write the equation:

L(8) = 8.8 + 5.1 log(8)

Here log means to take the logarithm (base 10) of the number in brackets. This takes a large number and returns its order of magnitude, e.g:

log (1000) = log (10^3) = 3

log (100) = log(10^2) = 2

log (0.01) = log(10^-2) = -2

To get the log of 8, you have to put it through a calculator, there's no easy way to get it by hand. You should get 0.903 for Log(8), and then the equation in full will give you 13.4.

If instead you find you get log(8) = 2.08, you are taking the natural logarithm instead of base 10. This is log to base e~2.7, usually denoted ln instead of log. Because it has a smaller base, it will give you a higher answer (since it's finding the exponent needed to raise the base to whatever number you put in, e.g. 8).

So be careful and make sure you're using the right base for the log!

Hope this was helpful and cleared things up a bit.

Mar 26th, 2015

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Mar 26th, 2015
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Mar 26th, 2015
May 22nd, 2017
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