Evaluate the expression without using a calculator In \( e^{4} \) \( \ln ^{4}=\square \)

To evaluate the expression \( e^{4} \) and express it in terms of \( \ln \), we start by recalling the relationship between the exponential function and the natural logarithm. The natural logarithm function \( \ln(x) \) is the inverse of the exponential function \( e^x \). This means that: \[ \ln(e^x) = x \] and \[ e^{\ln(x)} = x \] Now, we want to evaluate \( e^{4} \) in terms of \( \ln \). We can express \( e^{4} \) as follows: \[ e^{4} = e^{\ln(e^4)} = e^{\ln(e^4)} = e^{4} \] This doesn't change the expression, but it shows that \( e^{4} \) is simply \( e^{4} \). If we want to express \( e^{4} \) in terms of \( \ln \), we can use the fact that: \[ e^{4} = e^{\ln(e^4)} = e^{4} \] Thus, we can conclude that: \[ \ln(e^{4}) = 4 \] So, if we are looking for \( \ln^{4} \) in the context of the original question, it seems there might be a misunderstanding. The expression \( \ln^{4} \) is not standard notation. However, if we interpret it as \( \ln(e^{4}) \), we have: \[ \ln(e^{4}) = 4 \] Thus, the answer to the expression \( \ln^{4} \) is: \[ \boxed{4} \]