Questions: Convert to an exponential equation. ln 37=3.6109

Solution Steps

To convert a natural logarithm equation to an exponential equation, we use the property that if \(\ln a = b\), then \(a = e^b\). In this case, we have \(\ln 37 = 3.6109\), which can be rewritten in exponential form as \(37 = e^{3.6109}\).

We start with the equation given by the natural logarithm: \[ \ln 37 = 3.6109 \] Using the property of logarithms, we can convert this to its exponential form: \[ 37 = e^{3.6109} \]

Next, we compute the value of \(e^{3.6109}\): \[ e^{3.6109} \approx 36.9993 \]

Final Answer