91Ó°ÊÓ

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln \sqrt{x-8}=5$$

Use the properties of logarithms to expand the expression as a sum, difference, and or constant multiple of logarithms. (Assume all variables are positive.) $$\ln \frac{6}{\sqrt{x^{2}+1}}$$

Use a graphing utility to graph the exponential function. $$h(x)=e^{x-2}$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$2-6 \ln x=10$$

Use the acidity model given by \(\mathbf{p H}=-\log \left[\mathbf{H}^{+}\right],\) where acidity \((\mathbf{p H})\) is a measure of the hydrogen ion concentration \(\left[\mathbf{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. $$\text { Find the } \mathrm{pH} \text { when }\left[\mathrm{H}^{+}\right]=2.3 \times 10^{-5}$$.

Use the properties of logarithms to expand the expression as a sum, difference, and or constant multiple of logarithms. (Assume all variables are positive.) $$\ln \sqrt[3]{\frac{x}{y}}$$

Write the logarithmic equation in exponential form. $$\ln 250=5.521 \ldots$$

Use the One-to-One Property to solve the equation for \(x.\) $$e^{3 x+2}=e^{3}$$

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

Use the acidity model given by \(\mathbf{p H}=-\log \left[\mathbf{H}^{+}\right],\) where acidity \((\mathbf{p H})\) is a measure of the hydrogen ion concentration \(\left[\mathbf{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. $$\text { Find the } \mathrm{pH} \text { when }\left[\mathrm{H}^{+}\right]=1.13 \times 10^{-5}$$.