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# College Algebra #10

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The apparent brightness of a star observed from Earth is a logarithmic function of the intensity of the light arriving from the star. Astronomers use the magnitude scale to measure apparent brightness. The relative intensity I is calculated by forming the ratio of the intensity of light from the star Vega to the intensity of light from the star of interest. The magnitude m is then given by the following formula.

m = 2.5 log (I)

On the magnitude scale, higher magnitudes indicate dimmer stars.

(a) The light striking Earth from Vega is 2.9 times as bright as that from the star Fomalhaut. What is the apparent magnitude of Fomalhaut? (Round your answer to two decimal places.) __________?

(b) The star Antares has an apparent magnitude of 0.92. How does the intensity of light reaching Earth from Antares compare with that of light from Vega? (Round your answer to two decimal places.)

The intensity of light reaching Earth from Vega is I = _________?  times as intense as that from Antares.

(c) If the intensity of light striking Earth from one star is three times that of light from another, how do the stars' magnitudes compare? (Round your answer to two decimal places.)

The dimmer star has a magnitude of _________? more than that of the brighter star.

idenny  Apr 12, 2017
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a.  m Fomalhaut  =  2.5log(2.9)  ≈ 1.16

b.  0.92  =  2.5log (I)     divide both sides by  2.5

0.92/2.5  = log (I)      exponentially we have

10^(0.92/2.5)   = I   = 2.33 times as intense

CPhill  Apr 12, 2017
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Ugh I already had A and B but I just need C :(

idenny  Apr 12, 2017
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I did 2.5log(3) = 1.19

idenny  Apr 12, 2017
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# idenny

"Ugh I already had A and B but I just need C :("

Is this your way of saying "thank you" idenny?

You did not say anything about only wanting C when you asked the original question !

Melody  Apr 12, 2017
edited by Melody  Apr 12, 2017