Solve 1200(1.03)^x=800(1.08)^x

Question

I am not sure how to solve this. Someone please help.

Answer 1

1200(1.03^x) = 800(1.08^x)

divide by 800 on both sides

divide by 1.03^x on both sides

1200/800 = (1.08^x)/(1.03^x)

3/2 = (1.08/1.03)^x

ln(3/2) = ln( (1.08/1.03)^x )

ln(3/2) = x * ln(1.08/1.03)

Exact:  x = ln(3/2) / ln(1.08/1.03)

Decimal, approximate:  x = about 8.554