Questions: Convert to a logarithmic equation. e^5 = k

Solution Steps

To convert an exponential equation to a logarithmic equation, we use the property that if \( a^b = c \), then \( \log_a(c) = b \). In this case, the base of the exponential is \( e \), the exponent is \( 5 \), and the result is \( k \). Therefore, the logarithmic form of the equation is \( \log_e(k) = 5 \), which is also written as \( \ln(k) = 5 \).

We start with the exponential equation given by

\[ e^{5} = k. \]

To convert this to logarithmic form, we use the property that if \( a^b = c \), then \( \log_a(c) = b \). Here, we have:

\[ \log_e(k) = 5, \]

which can also be expressed as

\[ \ln(k) = 5. \]

Next, we calculate the value of \( k \) using the exponential function:

\[ k = e^{5}. \]

Evaluating this gives us:

\[ k \approx 148.4132. \]

Final Answer