I know the answer but I don't know the steps. Help needed, please!

We have

(1200(1-1.0216^n))/(1-1.0216)=10000   divide both sides by 1200

(1-1.0216^n))/(1-1.0216) =25/3    multiply both sides by (1-1.0216)

(1-1.0216^n)) = (25/3) (1-1.0216)     and 1-1.0216 = -.0216    .. so we have

(1-1.0216^n)) = -(25/3)(.0216)    rearrange

1.0216^n  = 1 + (25/3)(.0216)     and  1 + (25/3)(.0216) = 1.18    so we have

1.0216^n = 1.18    take the log of both sides

log 1.0216^n = log 1.18      and we can write

n log 1.0216  = log 1.18      divide both sides by log 1.0216

n = log(1.18) / log(1.0216)  = about 7.745

Thanks CPhill, you're awesome!