91Ó°ÊÓ

Complete the table to determine the balance \(A\) for \(\$ 12,000\) invested at rate \(r\) for \(t\) years, compounded continuously. $$ \begin{array}{|l|l|l|l|l|l|} \hline t & 10 & 20 & 30 & 40 & 50 \\ \hline A & & & & & \\ \hline \end{array} $$ $$r=6.5 \%$$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\ln \sqrt[4]{x^{3}\left(x^{2}+3\right)}$$

Write the exponential equation in logarithmic form. $$e^{x}=4$$

Use the following information for determining sound intensity. The level of sound \(\boldsymbol{\beta}\), in decibels, with an intensity of \(I\), is given by \(\boldsymbol{\beta}=10 \log \left(I / I_{0}\right),\) where \(I_{0}\) is an intensity of \(10^{-12}\) watt per square meter, corresponding roughly to the faintest sound that can be heard by the human ear. In Exercises 65 and 66 , find the level of sound \(\boldsymbol{\beta}\). (a) \(I=10^{-10}\) watt per \(\mathrm{m}^{2}\) (quiet room) (b) \(I=10^{-5}\) watt per \(\mathrm{m}^{2}\) (busy street corner) (c) \(I=10^{-8}\) watt per \(\mathrm{m}^{2}\) (quiet radio) (d) \(I=10^{0}\) watt per \(\mathrm{m}^{2}\) (threshold of pain)

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$\frac{119}{e^{6 x}-14}=7$$

Use the following information for determining sound intensity. The level of sound \(\boldsymbol{\beta}\), in decibels, with an intensity of \(I\), is given by \(\boldsymbol{\beta}=10 \log \left(I / I_{0}\right),\) where \(I_{0}\) is an intensity of \(10^{-12}\) watt per square meter, corresponding roughly to the faintest sound that can be heard by the human ear. In Exercises 65 and 66 , find the level of sound \(\boldsymbol{\beta}\). (a) \(I=10^{-11}\) watt per \(\mathrm{m}^{2}\) (rustle of leaves) (b) \(I=10^{2}\) watt per \(\mathrm{m}^{2}\) (jet at 30 meters) (c) \(I=10^{-4}\) watt per \(\mathrm{m}^{2}\) (door slamming) (d) \(I=10^{-2}\) watt per \(\mathrm{m}^{2}\) (siren at 30 meters)

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\ln \sqrt{x^{2}(x+2)}$$

Complete the table to determine the balance \(A\) for \(\$ 12,000\) invested at rate \(r\) for \(t\) years, compounded continuously. $$ \begin{array}{|l|l|l|l|l|l|} \hline t & 10 & 20 & 30 & 40 & 50 \\ \hline A & & & & & \\ \hline \end{array} $$ $$r=3.5 \%$$

Write the exponential equation in logarithmic form. $$e^{2 x}=3$$

Use a calculator to evaluate the function at the indicated value of \(x\). Round your result to three decimal places. $$ \begin{aligned} &\text { Function } \quad \text { Value }\\\ &f(x)=\ln x \quad x=18.42 \end{aligned} $$