Arrhenius equation may be represented as

Options

A. In `A/k=(E_(a))/(RT)`
B. `(d"In"K)/(dT)=(E_(a))/(RT)`
C. `logA=logk+(E_(a))/(2.303RT)`
D. `log(-(E_(a))/(Rt))=k/A`

Explanation

To solve the question regarding the representation of the Arrhenius equation, we will analyze the equation and its forms step by step.

### Step-by-Step Solution:

1. **Understanding the Arrhenius Equation**:
The Arrhenius equation is given by:
\[ k = A e^{-\frac{E_a}{RT}} \]
where:
- \( k \) = rate constant
- \( A \) = Arrhenius factor (pre-exponential factor)
- \( E_a \) = activation energy
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

2. **Taking the Natural Logarithm**:
To manipulate the equation, we can take the natural logarithm of both sides:
\[ \ln k = \ln A - \frac{E_a}{RT} \]

3. **Rearranging the Equation**:
Rearranging the above equation gives:
\[ \ln A - \ln k = \frac{E_a}{RT} \]
This can be rewritten as:
\[ \ln A = \ln k + \frac{E_a}{RT} \]
This form corresponds to option 3 in the question.

4. **Identifying Representable Forms**:
From the rearranged equation, we can see that:
- Option 1: \(\ln A - \ln k = \frac{E_a}{RT}\) can be rearranged to match our derived equation.
- Option 2: \( \frac{d \ln k}{dt} = \frac{A}{RT} \) does not represent the Arrhenius equation correctly.
- Option 3: \( \log A = \log k + \frac{E_a}{2.303RT} \) is a valid transformation of the Arrhenius equation.
- Option 4: \( \log \left(-\frac{E_a}{RT}\right) = k \) does not represent the Arrhenius equation.

5. **Conclusion**:
Based on the analysis, the correct representations of the Arrhenius equation are:
- Option 1: \(\ln A - \ln k = \frac{E_a}{RT}\)
- Option 3: \(\log A = \log k + \frac{E_a}{2.303RT}\)

### Final Answer:
The correct representations of the Arrhenius equation are options 1 and 3.