The magnitude of M of a star is a measure of its brightness B given by the formula M = -2.5 log (B/B0), where B0 is a constant, the brightness of an "average star."

a) If a star's brightness increases by a factor of 10, by how much does its magnitude increase or decrease?

I got the answer from the back of the book and it says "decreasing by -2.5." How did they get this answer? Please help me with this problem.

Thank you so much!

Increasing by a factor of 10 is a ratio of B0/B of 10/1 or 10.

LOG(10) = 1; Base 10 logarithm. The exponent of 10^x.

Thus M = -2.5*LOG(10) = -2.5