91Ó°ÊÓ

Solve for \(x\). Give any approximate results to three significant digits. Check your answers. $$\log 8 x^{2}-\log 4 x=2.54$$

Simplify each expression. $$\log _{10} 10$$

Solve for \(x\). Give any approximate results to three significant digits. Check your answers. $$2 \log x-\log (1-x)=1$$

In a certain fabric mill, cloth is removed from a dye bath and is then observed to dry exponentially at the rate of \(24 \%\) per hour. What percent of the original moisture will still be present after 5 h?

Find the half-life of a material that decays exponentially at the rate of \(3.50 \%\) per year.

Simplify each expression. $$\log _{3} 3^{2}$$

Simplify each expression. $$\log _{e} e^{x}$$

How long will it take the U.S. annual oil consumption to double if it is increasing exponentially at a rate of \(7.0 \%\) per year?

Computer: Assuming that the present annual world oil consumption is \(17 \times 10^{9}\) barrels/yr, that this rate of consumption is increasing at a rate of \(5 \%\) per year, and that the total world oil reserves are \(1700 \times 10^{9}\) barrels, compute and print the following table:$$\begin{array}{ccc}\hline \text { Year } & \text { Annual Consumption } & \text { Oil Remaining } \\\\\hline 0 & 17 & 1700 \\\1 & 17.85 & 1682.15 \\\& & \\\\\cdot & & \\ & &\end{array}$$,Have the computation stop when the oil reserves are almost gone.

How long will it take the world population to double at an exponential growth rate of \(1.64 \%\) per year?