Let I(A) stand for the intensity of light coming from star A. Let I(B) stand for the intensity of light coming from star B. We are told I(A) = 50 * I(B) So to calculate the magnitude difference, I(B) m(A) - m(B) = 2.5 * log10 ( ------- ) I(A) We replace I(A) with 50*I(B): I(B) m(A) - m(B) = 2.5 * log10 ( ------- ) 50*I(B) 1 = 2.5 * log10 ( ------- ) 50 = 2.5 * (-1.70) = -4.25 Now, we are told m(A) = 1.4. So 1.4 - m(B) = -4.25 - m(B) = -4.25 - 1.4 - m(B) = -5.65 m(B) = 5.65