Answer:
316227.766 kpc
Explanation:
Brightness is given by
[tex]B=\dfrac{L}{4\pi d^2}[/tex]
where
L = Luminosity of Sun
d = Distance to the Sun
[tex]d_1[/tex] = Distance to the supernova
[tex]L_1[/tex] = Luminosity of supernova = 10L
From the above relation we get
[tex]\dfrac{L_1}{4\pi d_1^2}=\dfrac{L}{4\pi d^2}\\\Rightarrow d_1=d\sqrt{\dfrac{L_1}{L}}\\\Rightarrow d_1=\sqrt{\dfrac{1\times 10^9L}{L}}\times 10\\\Rightarrow d_1=316227.766\ kpc[/tex]
The distance to the galaxy is 316227.766 kpc
