91Ó°ÊÓ

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$e^{2 x}+9 e^{x}+36=0$$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\log _{5} \frac{x^{2}}{y^{2} z^{3}}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$\frac{500}{100-e^{x / 2}}=20$$

Write the exponential equation in logarithmic form. $$e^{-0.9}=0.406 \ldots$$

Use the Richter scale \(R=\log \frac{l}{I_{0}}\) for measuring the magnitudes of earthquakes. Find the intensity \(I\) of an earthquake measuring \(R\) on the Richter scale (let \(I_{0}=1\) ). (a) Southern Sumatra, Indonesia in \(2007, R=8.5\) (b) Illinois in \(2008, R=5.4\) (c) Costa Rica in \(2009, R=6.1\)

Use the Richter scale \(R=\log \frac{l}{I_{0}}\) for measuring the magnitudes of earthquakes. Find the magnitude \(R\) of each earthquake of intensity \(I\) (let \(I_{0}=1\) ). (a) \(I=199,500,000\) (b) \(I=48,275,000\) (c) \(I=17,000\)

Write the exponential equation in logarithmic form. $$e^{-4.1}=0.0165 \ldots$$

Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.) $$\log _{10} \frac{x y^{4}}{z^{5}}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$\frac{400}{1+e^{-x}}=350$$

Solve the exponential equation algebraically. Approximate the result to three decimal places. $$\frac{3000}{2+e^{2 x}}=2$$