91Ó°ÊÓ

Write the exponential equation in logarithmic form. \(e^{2}=7.3890 \ldots\)

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. \(6 \log _{3}(0.5 x)=11\)

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.) $$\ln x^{2} \sqrt{\frac{y}{z}}$$

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 { Compute }\left[\mathrm{H}^{+}\right] \text {for a solution in which } \mathrm{pH}=5.8 $$

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

Write the exponential equation in logarithmic form. \(e^{1 / 2}=1.6487 \ldots\)

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. \(4 \log (x-6)=11\)

Using the One-to-One Property In Exercises \(51-54,\) use the One-to-One Property to solve the equation for \(x .\) $$e^{x^{2}+6}=e^{5 x}$$

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. $$ $$ $$ \text { Compute }\left[\mathrm{H}^{+}\right] \text {for a solution in which } \mathrm{pH}=3.2 $$

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.) $$\log _{2} x^{4} \sqrt{\frac{y}{z^{3}}}$$