solve the equation exactly for t

Question

  77e^0.17t=29(1.1)^t

Answer 1

The trick here is to recognize that (1.1)^t = e^ln(1.1)*t

77e^.17t = 29e^ln(1.1)*t

So 77/29 = e^{ln(1.1)*t-0.17t}

Or ln(77/29) = ln(1.1)*t - 0.17*t

Factor the t and solve.

Answer 2