91Ó°ÊÓ

Solve the equation. $$ x^{2} 2^{x}-2^{x}=0 $$

Use the Laws of Logarithms to expand the expression. $$ \log \left(\frac{x^{3} y^{4}}{z^{6}}\right) $$

The hydrogen ion concentration of a sample of each substance is given. Calculate the pH of the substance. (a) Lemon juice: \(\left[\mathrm{H}^{+}\right]=5.0 \times 10^{-3} \mathrm{M}\) (b) Tomato juice: \(\left[\mathrm{H}^{+}\right]=3.2 \times 10^{-4} \mathrm{M}\) (c) Seawater: \(\left[\mathrm{H}^{+}\right]=5.0 \times 10^{-9} \mathrm{M}\)

\(25-32\) Use the definition of the logarithmic function to find \(x\). $$ \begin{array}{ll}{\text { (a) } \log _{3} 243=x} & {\text { (b) } \log _{3} x=3}\end{array} $$

Use the Laws of Logarithms to expand the expression. $$ \log \left(\frac{a^{2}}{b^{4} \sqrt{c}}\right) $$

\(25-32\) Use the definition of the logarithmic function to find \(x\). $$ \begin{array}{ll}{\text { (a) } \log _{4} 2=x} & {\text { (b) } \log _{4} x=2}\end{array} $$

Solve the equation. $$ x^{2} 10^{x}-x 10^{x}=2\left(10^{x}\right) $$

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.

\(25-32\) Use the definition of the logarithmic function to find \(x\). $$ \begin{array}{ll}{\text { (a) } \log _{10} x=2} & {\text { (b) } \log _{5} x=2}\end{array} $$

Solve the equation. $$ 4 x^{3} e^{-3 x}-3 x^{4} e^{-3 x}=0 $$