15.23 b

[Andrea Grigsby 1I]

Why is the formula used for this question ln[A]0 / [A]t , instead of ln [A]t/[A]0?

[Angela 1K]

I used the equation and got the same answer as the solutions manual. I think the two equations are equivalent because of the negative sign I used in my answer, when transferred to the other side, would flip the two concentrations.

[David Zhou 1L]

It's just algebraic manipulation; flipping the numerator and denominator will give you the negative log value.

[Jenny Cheng 2K]

If you make both sides of the equation ln([A]t/[A]0) = -kt negative, you will have: ln([A]0/[A]t) = kt. Making the natural log negative flips the content because:
ln([A]t/[A]0) = ln[A]t - ln[A]0