First Order Integrated Law

[Tamera Scott 1G]

Why is the equation ln([A]t[A]0)=−kt also written as ln([A]0[A]t)=kt? Are they the same thing?

[Shubham Rai 2C]

The difference is probably due to what the [A] value is. The - is probably associated with reactants while the equation with the - is associated with products.

[Xinyi Zeng 4C]

They are the same thing!
ln([A]t/[A]0)=−kt can be written as ln([A]t)-ln([A]0)=-kt [ according to the log rule that ln(a/b)=ln(a)-ln(b) ]
multiply both sides of the equation by -1, you will get:
-ln([A]t)+ln([A]0)=kt, hence ln([A]0)-ln([A]t)=kt
applying the log rule again, you will get ln([A]0[A]t)=kt

[LeannaPhan14BDis1D]

Yes they are the same thing.