## Negative sign in ln [A]t = -k t + ln [A]o

$\frac{d[R]}{dt}=-k[R]; \ln [R]=-kt + \ln [R]_{0}; t_{\frac{1}{2}}=\frac{0.693}{k}$

Annie Chantasirivisal_4G
Posts: 114
Joined: Wed Sep 18, 2019 12:21 am

### Negative sign in ln [A]t = -k t + ln [A]o

For the formula ln [A]t = -k t + ln [A]o,

why is there a negative sign when t=-(1/k) ln[A]t/ln[A]o
but not when t=(1/k) ln[A]o/ln [A]t?

Sarah Zhari 1D
Posts: 103
Joined: Sat Sep 14, 2019 12:16 am

### Re: Negative sign in ln [A]t = -k t + ln [A]o

When you rearrange the equation ln [A]t = -k t + ln [A]o, you get ln [A]t-ln [A]o= -k t. Following the log rules, ln[A]t-ln[A]o is equal to ln([A]t/[A]o). Flipping the fraction to get ln([A]o/[A]t) is simply the negative, which explains the change in sign when you flip the fraction.