91Ó°ÊÓ

For the following exercises, evaluate the natural logarithmic expression without using a calculator. $$ 25 \ln \left(e^{\frac{2}{5}}\right) $$

For the following exercises, evaluate each expression using a calculator. Round to the nearest thousandth. $$ \log (0.04) $$

For the following exercises, evaluate each expression using a calculator. Round to the nearest thousandth. $$ \ln (15) $$

For the following exercises, evaluate each expression using a calculator. Round to the nearest thousandth. $$ \ln \left(\frac{4}{5}\right) $$

For the following exercises, evaluate each expression using a calculator. Round to the nearest thousandth. $$ \log (\sqrt{2}) $$

For the following exercises, evaluate each expression using a calculator. Round to the nearest thousandth. $$ \ln (\sqrt{2}) $$

Is \(f(x)=0\) in the range of the function \(f(x)=\log (x) ?\) If so, for what value of \(x ?\) Verify the result.

Is there a number \(x\) such that \(\ln x=2 ?\) If so, what is that number? Verify the result.

Is the following true: \(\frac{\log _{3}(27)}{\log _{4}\left(\frac{1}{64}\right)}=-1 ?\) Verify the result.

The exposure index \(E I\) for a 335 millimeter camera is a measurement of the amount of light that hits the film. It is determined by the equation \(E I=\log _{2}\left(\frac{f^{2}}{t}\right),\) where \(f\) is the "f-stop" setting on the camera, and \(t\) is the exposure time in seconds. Suppose the f-stop setting is 8 and the desired exposure time is 2 seconds. What will the resulting exposure index be?