91Ó°ÊÓ

Use the definition of the logarithmic function to find \(x\) $$ \begin{array}{ll}{\text { (a) } \log _{2} x=5} & {\text { (b) } \log _{2} 16=x}\end{array} $$

\(19-44\) Use the Laws of Logarithms to expand the expression. $$ \log _{5} \sqrt[3]{x^{2}+1} $$

Use the definition of the logarithmic function to find \(x\) $$ \begin{array}{ll}{\text { (a) } \log _{3} x=4} & {\text { (b) } \log _{10} 0.1=x}\end{array} $$

\(29-43\) . These exercises deal with logarithmic scales. Finding \(\mathrm{pH}\) An unknown substance has a hydrogen ion concentration of \(\left[\mathrm{H}^{+}\right]=3.1 \times 10^{-8} \mathrm{M} .\) Find the pH and classify the substance as acidic or basic.

Solve the equation. \(e^{2 x}-e^{x}-6=0\)

\(19-44\) Use the Laws of Logarithms to expand the expression. $$ \log _{a}\left(\frac{x^{2}}{y z^{3}}\right) $$

Compound Interest If \(\$ 2000\) is invested at an interest rate of 3.5\(\%\) per year, compounded continuously, find the value of the investment after the given number of years. \(\begin{array}{llll}{\text { (a) } 2 \text { years }} & {\text { (b) } 4 \text { years }} & {\text { (c) } 12 \text { years }}\end{array}\)

\(19-44\) Use the Laws of Logarithms to expand the expression. $$ \ln \sqrt{a b} $$

Solve the equation. \(e^{4 x}+4 e^{2 x}-21=0\)

\(29-43\) . These exercises deal with logarithmic scales. Ion Concentration The pH reading of a sample of each substance is given. Calculate the hydrogen ion concentration of the substance. (a) Vinegar: pH \(=3.0\) (b) Milk: \(\mathrm{pH}=6.5\)