I need help on part b The apparent magnitude M of a celestial body can be approx

Question

I need help on part b

The apparent magnitude M of a celestial body can be approximated by the formula M = 6 -2.5 log I/I_0 where I is the intensity of its light, as measured from Earth, and I_0 is the approximate intensity of the light of the faintest stars visible to the naked eye from Earth. a. Find M if I = 0.001 and I_0 = 1. M = 13.5 (Type an integer or a decimal rounded to the nearest tenth as needed.) b. What is the apparent magnitude of a star whose light, as measured from Earth, is 1000 times as intense as that of the faintest star visible to the naked eye? (Type an integer or a decimal rounded to the nearest tenth as needed.)

Explanation / Answer

(b) given : I = 1000 I0

By formula

M = 6- 2.5 log (1000I0/I0)

= 6-2.5 log(1000)

= 6-7.5

= -1.5

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