# Thread: Logarithmic Problem

1. ## Logarithmic Problem

The stellar magnitude scale compares the brightness of stars using the equation m1 - m2 = log(base 10) (b1 / b2). Sirius is the brightest star appearing in our sky, with a magnitude of 1.5. How much brighter does Sirius appear than Neptune, whose apparent magnitude is 0.12.
How do we approach this when we have 4 variables and only given 2 ?

1.5 - 0.12 = log(base 10) (b1 / b2) then what?

2. ## Re: Logarithmic Problem

Originally Posted by sakonpure6
How do we approach this when we have 4 variables and only given 2 ?

1.5 - 0.12 = log(base 10) (b1 / b2) then what?
you only have 1 variable here really.

you are given m2 and m1.

If you had to find b1 and b2 separately you would have two variables but the question just asks for their ratio.

$1.5 - 0.12 = log_{10}\frac{b1}{b2}$

$1.38= log_{10}\frac{b1}{b2}$

$10^{1.38}=\frac{b1}{b2}$

and that's all you can say, i.e. that Sirius has apparent brightness $10^{1.38}$ times that of Neptune

3. ## Re: Logarithmic Problem

Think of b1 over b2 as a fixed ratio. Find the ratio. I think it's easy to go from there.