Question 502982
You want to solve the following equation for t

{{{4e^(3t+5)}}} = {{{4/(e^t)}}}

Remember when you multiply, you add exponents, so multiply both sides of the equation by {{{e^t}}}, and then divide by 4

{{{4(e^(3t+5))}}}{{{e^t}}} = 4

{{{e^(4t+5)}}} = 1

To simplify an exponential function take the logarithm (ln) of both sides

{{{ln(e^(4t+5))}}} = ln(1) = 0

By definition  {{{ln(e^(x))}}} = x, and ln(1) = 0, so

4t + 5 = 0

4t = -5

t = -5/4 = - 1.25