How to rearrange the given equation for A: ln (Ao/A) = k*t

Multiply both sides by A then divide by kt

A = Ao/kt

I am assuming the * means multiplication.

what about the ln? (natural log)

ln(Ao/A)=kt => (Ao/A)=e^kt

=> Ao/e^kt=A => A=Aoe^-kt (1st order integrated rate law)

To rearrange the given equation for A, ln(Ao/A) = k*t, we can follow the steps below:

Step 1: Begin with the original equation:
ln(Ao/A) = k*t

Step 2: Apply the property of natural logarithm to eliminate the natural logarithm from the equation:
Ao/A = e^(k*t) (where e is the base of the natural logarithm)

Step 3: Cross-multiply to isolate A:
A*e^(k*t) = Ao

Step 4: Divide both sides of the equation by e^(k*t):
A = Ao / e^(k*t)

Therefore, the rearranged equation for A is A = Ao / e^(k*t).