First Order Integrated Rate Laws

[Amy Luu 2G]

When the problem asks for the time it takes for a reaction to decay why do we use the equation t= (1/k_r)*ln([A]₀/[A]_t)? Isnt there supposed to be a negative sign if we solve for t using ln([A]₀/[A]_t)= -k_rt?

[Justin Seok 2A]

I believe it may be the way that ln works with negatives, since -ln([A]t/[A]0) would be equivalent to ln([A]0/[A]t). So the equation would go from [A]t=[A]0*(e^(-kt)) to [A]t/[A]0 = e^-kt to ln([A]t/[A]0) = -kt to t = ln([A]0/[A]t)/k.