Question

5 e^-(t/5^2) = 1.5
e^-(t/125) = .3
e^(t/125) = 1/.3 = 3.3333
t/125 = ln 3.3333
t = 150.5

can some one please explain why it's 1/.3 and where the one comes from and where the negative sign goes.

Steps 2 to 3 is what i'm talking about

Answer 1

first of all, from line 1 to line 2 , 5^2 = 25 not 125.

So I don't know where the typo is, since the 125 is carried all the way from there.

from line 2 to line 3, the negative exponent rule was used, i.e.
if a^-n = p/q then
a^+n = q/p

illustrating with an example
2^-3 = 1/8
2^+3 = 8/1 or 8

if you first line was styped correctly then your solution would be
t/25 = ln 3.33333..
t = 83.3333.. or 83 1/3