Question
Given the following logarithmic function below, what is the value of \( f(2) \) (round to the nearest hundredth)? \( f(x)=\ln x \) 1.69 0.69 0.89 0.77
Ask by Reid Medina. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( f(2) \approx 0.69 \)
Solution
To find the value of \( f(2) \) for the given logarithmic function \( f(x) = \ln x \), we substitute \( x = 2 \) into the function.
Given:
\[ f(x) = \ln x \]
Substitute \( x = 2 \):
\[ f(2) = \ln 2 \]
To find the value of \( f(2) \), we need to calculate \( \ln 2 \).
Let's calculate \( \ln 2 \) using a calculator or a logarithmic table.
Calculate the value by following steps:
- step0: Calculate:
\(\ln{\left(2\right)}\)
The value of \( \ln 2 \) is approximately 0.693147.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the value of \( f(2) \) for the function \( f(x) = \ln x \), we need to calculate \( \ln 2 \). Using a calculator, we find that \( \ln 2 \approx 0.693 \). Rounding to the nearest hundredth gives us 0.69. So, the correct answer is 0.69! Let's celebrate the beauty of logarithms and their applications in real life—from measuring sound intensity in decibels to calculating the pH levels in chemistry, logarithmic functions truly help us understand the world in exponential ways (pun intended)!
