Chapter 4

For the following exercises, rewrite each equation in exponential form. $$\log _{13}(142)=a$$

For the following exercises, rewrite each equation in exponential form. $$\log (v)=t$$

For the following exercises, rewrite each equation in exponential form. $$\ln (w)=n$$

For the following exercises, rewrite each equation in logarithmic form. $$4^{x}=y$$

For the following exercises, rewrite each equation in logarithmic form. $$c^{d}=k$$

For the following exercises, rewrite each equation in logarithmic form. $$m^{-7}=n$$

For the following exercises, rewrite each equation in logarithmic form. $$19^{x}=y$$

For the following exercises, rewrite each equation in logarithmic form. $$x^{-\frac{10}{13}}=y$$

For the following exercises, rewrite each equation in logarithmic form. $$ n^{4}=103 $$

For the following exercises, rewrite each equation in logarithmic form. $$ \left(\frac{7}{5}\right)^{m}=n $$

For the following exercises, rewrite each equation in logarithmic form. $$ y^{x}=\frac{39}{100} $$

For the following exercises, rewrite each equation in logarithmic form. $$ 10^{a}=b $$

For the following exercises, rewrite each equation in logarithmic form. $$ e^{k}=h $$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log _{3}(x)=2$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log _{2}(x)=-3$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log _{5}(x)=2$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log _{3}(x)=3$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log _{2}(x)=6$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log _{9}(x)=\frac{1}{2}$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log _{18}(x)=2$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log _{6}(x)=-3$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\log (x)=3$$

For the following exercises, solve for \(x\) by converting the logarithmic equation to exponential form. $$\ln (x)=2$$

For the following exercises, use the definition of common and natural logarithms to simplify. $$\log \left(100^{8}\right)$$

For the following exercises, use the definition of common and natural logarithms to simplify. $$10^{\log (32)}$$

For the following exercises, use the definition of common and natural logarithms to simplify. $$2 \log (.0001)$$

For the following exercises, use the definition of common and natural logarithms to simplify. $$e^{\ln (1.06)}$$

For the following exercises, use the definition of common and natural logarithms to simplify. $$\ln \left(e^{-5.03}\right)$$

For the following exercises, use the definition of common and natural logarithms to simplify. $$e^{\ln (10.125)}+4$$

For the following exercises, evaluate the base \(b\) logarithmic expression without using a calculator. $$\log _{3}\left(\frac{1}{27}\right)$$

For the following exercises, evaluate the base \(b\) logarithmic expression without using a calculator. $$\log _{6}(\sqrt{6})$$

For the following exercises, evaluate the base \(b\) logarithmic expression without using a calculator. $$\log _{2}\left(\frac{1}{8}\right)+4$$

For the following exercises, evaluate the base \(b\) logarithmic expression without using a calculator. $$6 \log _{8}(4)$$

For the following exercises, evaluate the common logarithmic expression without using a calculator. $$ \log (10,000) $$

For the following exercises, evaluate the common logarithmic expression without using a calculator. $$ \log (0.001) $$

For the following exercises, evaluate the common logarithmic expression without using a calculator. $$ \log (1)+7 $$

For the following exercises, evaluate the common logarithmic expression without using a calculator. $$ 2 \log \left(100^{-3}\right) $$

For the following exercises, evaluate the natural logarithmic expression without using a calculator. $$ \ln \left(e^{\frac{1}{3}}\right) $$

For the following exercises, evaluate the natural logarithmic expression without using a calculator. $$ \ln (1) $$

For the following exercises, evaluate the natural logarithmic expression without using a calculator. $$ \ln \left(e^{-0.225}\right)-3 $$

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?