Question
Express \( e^{2}=7.389 \) in logarithmic form. \( \begin{array}{ll}\text { a. } \quad \log _{2} 7.389=e & \text { b. } \quad \log _{7.389}(e)=2 \\ \text { c. } \quad \ln 7.389=2 & \text { d. } \quad \ln 2=7.389\end{array} \)
Ask by Rojas Jimenez. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The correct logarithmic form is \( \ln 7.389 = 2 \).
Solution
To convert the exponential equation \( e^{2} = 7.389 \) into logarithmic form, we use the definition of a logarithm:
\[
a^b = c \quad \text{is equivalent to} \quad \log_{a} c = b
\]
Here, \( a = e \), \( b = 2 \), and \( c = 7.389 \). Applying the definition:
\[
\log_{e} 7.389 = 2
\]
Since \( \log_{e} \) is the natural logarithm, denoted as \( \ln \), the equation becomes:
\[
\ln 7.389 = 2
\]
**Correct Answer:**
**c.** \( \ln 7.389 = 2 \)
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Simplify this solution Bonus Knowledge
To express \( e^{2} = 7.389 \) in logarithmic form, we can rewrite it as \( \ln(7.389) = 2 \). This corresponds to option **c**. So, the correct expression in logarithmic form is: \[ \ln(7.389) = 2 \] Hence, the answer is **c. \(\ln 7.389=2\)**. For extra clarity, remember that \( \ln(x) \) is the natural logarithm, meaning it's the logarithm with base \( e \)! This is particularly useful in calculus and any application involving continuous growth or decay, where \( e \) naturally arises.
