Given the following logarithmic function below, what is the value of \( f(0.1) \) (round to the nearest hundredth)? \( f(x)=\ln x \) -5.30 -4.30 -3.30

To find the value of \( f(0.1) \) for the function \( f(x) = \ln x \), we compute \( f(0.1) = \ln(0.1) \). Using the properties of logarithms, \( \ln(0.1) \) can be rewritten as \( \ln(10^{-1}) = -1 \cdot \ln(10) \). Given that \( \ln(10) \approx 2.30 \), we find \( f(0.1) \approx -2.30 \). So rounding to the nearest hundredth, the answer is approximately -2.30. Exploring logarithms can be particularly fun since they show how we can turn multiplication into addition! Recognizing that logarithm properties such as \( \ln(a \cdot b) = \ln a + \ln b \) allow you to break down complex problems makes them powerful tools, especially in solving exponential equations. A common mistake when working with logarithms is misinterpreting the domain. Remember, \( \ln x \) is only defined for \( x > 0 \). So any value of \( x \leq 0 \) won't work, which is an easy slip to make when venturing into the world of functions and their properties.