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Old Mar 23rd 2016, 05:58 PM   #1
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I am having a little trouble understanding some maths in a problem involving the surface brightness of galaxies.

I know of the theory behind the problem but I don't know where exactly one step comes from in terms of the maths.

In the attachment, from the first to the second line, it goes from -2.5log(e^-7.67[………etc.,) on the first line to 7.67log e x [(R\Re)^1\4 -1] on the second line.

I was hoping maybe someone could show me this step done properly so that I can understand the mathematics.
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Old Mar 23rd 2016, 06:57 PM   #2
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Originally Posted by Clyner82 View Post
I am having a little trouble understanding some maths in a problem involving the surface brightness of galaxies.

I know of the theory behind the problem but I don't know where exactly one step comes from in terms of the maths.

In the attachment, from the first to the second line, it goes from -2.5log(e^-7.67[………etc.,) on the first line to 7.67log e x [(R\Re)^1\4 -1] on the second line.

I was hoping maybe someone could show me this step done properly so that I can understand the mathematics.
It uses the law: log(ab) = log(a) + log(b). Here we have a = I_e and b = e^(-7.76 ((R/R_e)^(1/4)-1)

-Dan
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Old Mar 23rd 2016, 07:47 PM   #3
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I am still not seeing how you get from step 1 to step 2
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Old Mar 24th 2016, 08:17 AM   #4
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C-2.5 log I_c is apparently a constant, so that becomes "const" in line 2.

They also use the principle that log a^b = b log a. In this case b = that rather complicated expression, which for some reason they break in two and put part of it in front of the log term and some after. In essence it's this:

log a^(bc) = b x c x (log a) = b x (log a) x c

Last edited by ChipB; Mar 24th 2016 at 01:30 PM.
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Old Mar 24th 2016, 08:39 AM   #5
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Thanks a millions Chip, that makes more sense now.

Much appreciate your time in helping me out.
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