91Ó°ÊÓ

Levels In Exercises \(51-56,\) use the acidity model given by \(\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right],\) where acidity \((\mathrm{pH})\) is a measure of the hydrogen ion concentration \(\left[\mathbf{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. $$ \text { Find the } \mathrm{pH} \text { when }\left[\mathrm{H}^{+}\right]=2.3 \times 10^{-5} $$

Expanding a Logarithmic Expression In Exercises \(37-58\) , 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. \(\ln 250=5.521 \ldots\)

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

Using the One-to-One Property In Exercises \(51-54,\) use the One-to-One Property to solve the equation for \(x .\) $$e^{3 x+2}=e^{3}$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. \(2+3 \ln x=12\)

Using the One-to-One Property In Exercises \(51-54,\) use the One-to-One Property to solve the equation for \(x .\) $$e^{2 x-1}=e^{4}$$

Write the logarithmic equation in exponential form. \(\ln 1=0\)

Levels In Exercises \(51-56,\) use the acidity model given by \(\mathrm{pH}=-\log \left[\mathrm{H}^{+}\right],\) where acidity \((\mathrm{pH})\) is a measure of the hydrogen ion concentration \(\left[\mathbf{H}^{+}\right]\) (measured in moles of hydrogen per liter) of a solution. $$ \text { Find the } \mathrm{pH} \text { when }\left[\mathrm{H}^{+}\right]=1.13 \times 10^{-5} $$

Expanding a Logarithmic Expression In Exercises \(37-58,\) use the properties of logarithms to expand the expression as a sum, difference, and or constant multiple of logarithms. (Assume all variables are positive.) $$\ln \sqrt{\frac{x^{2}}{y^{3}}}$$