Light from one star is 40 times more intense than light from another star, whats the diff in magnitude?

Question

I know that the light from Sirius is 24.2 times more intense than light from Polaris and their difference in magnitude is 3.4

So how about if a star is 40 times more intense? Would the difference in magnitude be 4?

Thank you

Answer 1

4 magnitudes.

Each magnitude is 2.512 times the next, and 2.512^4 is about 40. 5 magnitudes is 100.