Question

At what distance does a star have an apparent magnitude that is 5 magnitudes brighter (smaller) than its absolute magnitude?

Answer 1

Let's apply the formula

$M=m+5-5 \lg{(r)}$

Where

$M-$ absolute magnitude

$m-$ apparent magnitude

where do we write

$M-m=5-5 \lg{(r)}$

by problem statement

$M-m=5$

then

$5=5-5 \lg{(r)}$

$5-5=-5 \lg{(r)}$

$0=-5 \lg{(r)}$

$0=\lg{(r)}$

from where

$r=1 pc$