Question

given the equation $\ln a = \ln a_0 - kt$, rearrange the equation to solve for $k$. answer options: $k = (\ln a_0 - \ln a)/t$, $k = \ln a_0 - (\ln a)/t$, $k = (\ln a_0 + \ln a)/t$, $k = t/(\ln a_0 - \ln a)$, $k = \ln a - (\ln a_0)/t$, i dont know yet

Explanation:

Step1: Start with the given equation

We have the equation $\ln A = \ln A_0 - kt$.

Step2: Isolate the term with \( k \)

First, we can rearrange the equation to get \( kt = \ln A_0 - \ln A \). This is done by adding \( kt \) to both sides and subtracting \( \ln A \) from both sides of the original equation.

Step3: Solve for \( k \)

Now, divide both sides of the equation \( kt = \ln A_0 - \ln A \) by \( t \) (assuming \( t
eq0 \)) to solve for \( k \). We get \( k=\frac{\ln A_0 - \ln A}{t} \).

Answer:

\( k = \frac{\ln A_0 - \ln A}{t} \) (corresponding to the option \( k = (\ln A_0 - \ln A)/t \))