SOLUTION: Magnitude of a Star The magnitude M of a star is modeled by: M=6-5over2 log I over I subscript 0 Where I subscript 0 is the intensity of a just visible star and I is the actual

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Magnitude of a Star The magnitude M of a star is modeled by: M=6-5over2 log I over I subscript 0 Where I subscript 0 is the intensity of a just visible star and I is the actual       Log On


   

Question 548456: Magnitude of a Star
The magnitude M of a star is modeled by:
M=6-5over2 log I over I subscript 0
Where I subscript 0 is the intensity of a just visible star and I is the actual itensity of the star being measured. The dimmest stars are of a magnitude 6, and the brightest are of a magnitude 1. Determine the ratio of light intensities between a star of magnitude 1 and a star of magnitude 6.
NOTE: 5 over 2 is a fraction and I over I subscript 0 is a fraction. The log is inbetween both fractions.
I really need help with this problem as I cannot even know where to begin on it. I would greatly appreciate the help.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I assume you meant M=6-%285%2F2%29log%28I%2FI%5B0%5D%29
For a star of magnitude 1,
1=6-%285%2F2%29log%28I%2FI%5B0%5D%29 --> 1-6=-%285%2F2%29log%28I%2FI%5B0%5D%29 --> -5=-%285%2F2%29log%28I%2FI%5B0%5D%29
Sorry, if I'm going to slow. I'd rather err on the side of over-explaining.
Then 5=%285%2F2%29log%28I%2FI%5B0%5D%29 --> 1=%281%2F2%29log%28I%2FI%5B0%5D%29 --> 2=log%28I%2FI%5B0%5D%29 --> 10%5E2=100=I%2FI%5B0%5D --> I=100%2AI%5B0%5D
For a star of magnitude 6,
6=6-%285%2F2%29log%28I%2FI%5B0%5D%29 --> 6-6=-%285%2F2%29log%28I%2FI%5B0%5D%29 --> 0=-%285%2F2%29log%28I%2FI%5B0%5D%29
So 0=log%28I%2FI%5B0%5D%29 --> 10%5E0=1=I%2FI%5B0%5D --> I=I%5B0%5D
So the light from a star of magnitude 1 is 100 times more intense than the light from a star of magnitude 6.