Question
4
Evaluate the following logarithmic expression:
ln
e
7
lne
7
Evaluate the following logarithmic expression:
ln
e
7
lne
7
Answers
Answered by
GPT-4o mini
To evaluate the expression \( \ln(e^7) \), we can use the property of logarithms that states:
\[
\ln(a^b) = b \cdot \ln(a)
\]
Here, \( a = e \) and \( b = 7 \). Since the natural logarithm of \( e \) (i.e., \( \ln(e) \)) is equal to 1, we can simplify:
\[
\ln(e^7) = 7 \cdot \ln(e) = 7 \cdot 1 = 7
\]
Thus, the value of \( \ln(e^7) \) is:
\[
\boxed{7}
\]
\[
\ln(a^b) = b \cdot \ln(a)
\]
Here, \( a = e \) and \( b = 7 \). Since the natural logarithm of \( e \) (i.e., \( \ln(e) \)) is equal to 1, we can simplify:
\[
\ln(e^7) = 7 \cdot \ln(e) = 7 \cdot 1 = 7
\]
Thus, the value of \( \ln(e^7) \) is:
\[
\boxed{7}
\]