Katsuo M. answered 03/28/21
Experienced Engineer Tutoring Algebra & Geometry
We can solve for years t with the equations
BJ = 500*1.03t
BD = 100*1.12t
Using log identities, we can isolate t as follows:
100*1.12t > 500*1.03t
1.12t > 5*1.03t
t*log(1.12) > log(5) + t*log(1.03)
t*(log(1.12) - log(1.03)) > log(5)
t > log(5)/(log(1.12) - log(1.03))
t > 19.21
Thus, it will take 20 years. (Check it by plugging it into the equations above.)