91Ó°ÊÓ

Find the number whose common logarithm is given. $$1.584$$

A flywheel is rotating at a speed of 1805 rev/min. When the power is disconnected, the speed decreases exponentially at the rate of \(32.0 \%\) per minute. Find the speed after 10.0 min.

Rewrite each equation so that it contains no logarithms. $$\log x+3 \log y=0$$

Solve for \(x\). Give any approximate results to three significant digits. Check your answers. $$\ln x-2 \ln x=\ln 64$$

Solve for \(x\). Give any approximate results to three significant digits. Check your answers. $$\ln 6+\ln (x-2)=\ln (3 x-2)$$

A steel forging is \(1495^{\circ} \mathrm{F}\) above room temperature. If it cools exponentially at the rate of \(2.00 \%\) per minute, how much will its temperature drop in \(1 \mathrm{h} ?\)

Rewrite each equation so that it contains no logarithms. $$2 \log (x-1)=5 \log (y+2)$$

As light passes through glass or water, its intensity decreases exponentially according to the equation $$I=I_{0} e^{-k x}$$,where \(I\) is the intensity at a depth \(x\) and \(I_{0}\) is the intensity before entering the glass or water. If, for a certain filter glass, \(k=0.500 / \mathrm{cm}\) (which means that each centimeter of filter thickness removes half the light reaching it), find the fraction of the original intensity that will pass through a filter glass \(2.00 \mathrm{cm}\) thick.

The barometric pressure in inches of mercury at a height of \(h\) feet above sea level is $$p=30.0 e^{-k h}$$ where \(k=3.83 \times 10^{-5} .\) At what height will the pressure be 10.0 in. of mercury?

The approximate density of seawater at a depth of \(h\) mi is $$d=64.0 e^{0.00676 h}\left(\mathrm{lb} / \mathrm{ft}^{3}\right)$$ Find the depth \(h\) at which the density will be \(64.5 \mathrm{lb} / \mathrm{ft}^{3}.\)