Question

Magnitude of Stars The magnitude $M$ of a star is a measure of how bright a star appears to the human eye. It is defined by \[ M=-2.5 \log \left(\frac{B}{B_{0}}\right) \] where $B$ is the actual brightness of the star and $B_{0}$ is a constant. (a) Expand the right-hand side of the equation. (b) Use part (a) to show that the brighter a star, the less its magnitude. (c) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero.

Name: Problem 75, Chapter 4: College Algebra
Uploaded: 2020-08-06T06:54:23-08:00
Duration: 2 min 55 s
Channel: Ankit Gupta

   Magnitude of Stars The magnitude $M$ of a star is a measure of how bright a star appears to the human eye. It is defined by
\[
M=-2.5 \log \left(\frac{B}{B_{0}}\right)
\]
where $B$ is the actual brightness of the star and $B_{0}$ is a constant.
(a) Expand the right-hand side of the equation.
(b) Use part (a) to show that the brighter a star, the less its magnitude.
(c) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero.

College Algebra

James Stewart,… 7th Edition

Chapter 4, Problem 75

Instant Answer

Solved by Expert Ankit Gupta

08/06/2020

Step 1

5 \log \left(\frac{B}{B_{0}}\right)$. We can use the property of logarithms that $\log(a/b) = \log a - \log b$ to rewrite the right-hand side of the equation. Show more…

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Magnitude of Stars The magnitude $M$ of a star is a measure of how bright a star appears to the human eye. It is defined by \[ M=-2.5 \log \left(\frac{B}{B_{0}}\right) \] where $B$ is the actual brightness of the star and $B_{0}$ is a constant. (a) Expand the right-hand side of the equation. (b) Use part (a) to show that the brighter a star, the less its magnitude. (c) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero.

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