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Express \( \ln 3=1.099 \) in exponential form. \( \begin{array}{ll}\text { a. } 10^{3}=1.099 & \text { b. } e^{1.099}=3 \\ \text { c. } e^{3}=1.099 & \text { d. } \\ l n & \ln (1.099)=3\end{array} \)

Ask by Blake Clarke. in the United States
Feb 03,2025

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Answer

\( e^{1.099} = 3 \)

Solution

To express the logarithmic equation \( \ln 3 = 1.099 \) in exponential form, we use the relationship between logarithms and exponents. Recall that if \( \ln a = b \), then the exponential form is \( e^b = a \). Applying this to the given equation: \[ \ln 3 = 1.099 \quad \Rightarrow \quad e^{1.099} = 3 \] So, the correct exponential form is: **b. \( e^{1.099} = 3 \)**

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To express \( \ln 3 = 1.099 \) in exponential form, we need to remember that the natural logarithm function \( \ln \) is the inverse of the exponential function \( e^x \). This means that if \( \ln a = b \), then \( e^b = a \). Therefore, from \( \ln 3 = 1.099 \), we can convert it to: \[ e^{1.099} = 3. \] So the correct option is \( \text{b. } e^{1.099} = 3 \). If you're ever in doubt, just remember: when you see \( \ln \) on one side, the base 'e' will be on the other side, connecting the dots from logarithm to exponential form!

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