Chapter 6

For each statement, write an equivalent statement in logarithmic form. Do not use a calculator. $$3^{4}=81$$

Decide whether each function is one-to-one. $$f(x)=-3 x+5$$

Solve each equation. Express all solutions in exact form. Do not use a calculator. $$3 e^{2 x}+1=5$$

Graph each function. Do not use a calculator. $$f(x)=3^{x}$$

For each statement, write an equivalent statement in logarithmic form. Do not use a calculator. $$2^{5}=32$$

Decide whether each function is one-to-one. $$f(x)=-5 x+2$$

Solve each equation. Express all solutions in exact form. Do not use a calculator. $$\frac{1}{2} e^{x}=13$$

Graph each function. Do not use a calculator. $$f(x)=4^{x}$$

For each statement, write an equivalent statement in logarithmic form. Do not use a calculator. $$\left(\frac{1}{2}\right)^{-4}=16$$

Solve each equation. Express all solutions in exact form. Do not use a calculator. $$2\left(10^{x}\right)=14$$

Graph each function. Do not use a calculator. $$f(x)=\left(\frac{1}{3}\right)^{x}$$

For each statement, write an equivalent statement in logarithmic form. Do not use a calculator. $$\left(\frac{2}{3}\right)^{-3}=\frac{27}{8}$$

Decide whether each function is one-to-one. $$f(x)=-x^{2}$$

Solve each equation. Express all solutions in exact form. Do not use a calculator. $$5\left(10^{3 x}\right)-4=6$$

Graph each function. Do not use a calculator. $$f(x)=\left(\frac{1}{4}\right)^{x}$$

Decide whether each function is one-to-one. $$f(x)=\sqrt{36-x^{2}}$$

For each statement, write an equivalent statement in logarithmic form. Do not use a calculator. $$10^{-4}=0.0001$$

Solve each equation. Express all solutions in exact form. Do not use a calculator. $$\frac{1}{2} \log _{2} x=\frac{3}{4}$$

Solve each equation. Do not use a calculator. $$4^{x}=2$$

Decide whether each function is one-to-one. $$f(x)=-\sqrt{100-x^{2}}$$

For each statement, write an equivalent statement in logarithmic form. Do not use a calculator. $$\left(\frac{1}{100}\right)^{-2}=10,000$$

Solve each equation. Express all solutions in exact form. Do not use a calculator. $$2 \log _{3} x=\frac{4}{5}$$

Solve each equation. Do not use a calculator. $$125^{x}=5$$

Decide whether each function is one-to-one. $$f(x)=x^{3}$$

For each statement, write an equivalent statement in logarithmic form. Do not use a calculator. $$e^{0}=1$$

Solve each equation. Express all solutions in exact form. Do not use a calculator. $$4 \ln 3 x=8$$

Solve each equation. Do not use a calculator. $$\left(\frac{1}{2}\right)^{x}=4$$

Decide whether each function is one-to-one. $$f(x)=\sqrt[3]{x}$$

For each statement, write an equivalent statement in logarithmic form. Do not use a calculator. $$e^{1 \Omega}=\sqrt[3]{e}$$

Solve each equation. Express all solutions in exact form. Do not use a calculator. $$7 \ln 2 x=10$$

Solve each equation. Do not use a calculator. $$\left(\frac{2}{3}\right)^{x}=\frac{9}{4}$$

Decide whether each function is one-to-one. $$f(x)=|2 x+1|$$

For each statement, write an equivalent statement in exponential form. Do not use a calculator. $$\log _{6} 36=2$$

Solve each exponential equation. Express the solution set so that (a) solutions are in exact form and, if irrational, (b) solutions are approximated to the nearest thousandth. Support your solutions by using a calculator. $$3^{x}=7$$

Use a calculator to find an approximation for each power. Give the maximum number of decimal places that your calculator displays. $$2^{\sqrt{10}}$$

Can a quadratic function \(f\) with domain \((-\infty, \infty)\) have an inverse function? Explain.

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log \frac{1}{2} x$$

For each statement, write an equivalent statement in exponential form. Do not use a calculator. $$\log _{5} 5=1$$

Solve each exponential equation. Express the solution set so that (a) solutions are in exact form and, if irrational, (b) solutions are approximated to the nearest thousandth. Support your solutions by using a calculator. $$5^{x}=13$$

Use a calculator to find an approximation for each power. Give the maximum number of decimal places that your calculator displays. $$3^{\sqrt{11}}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log (-x)$$

For each statement, write an equivalent statement in exponential form. Do not use a calculator. $$\log \sqrt{3} 81=8$$

Solve each exponential equation. Express the solution set so that (a) solutions are in exact form and, if irrational, (b) solutions are approximated to the nearest thousandth. Support your solutions by using a calculator. $$\left(\frac{1}{2}\right)^{x}=5$$

Use a calculator to find an approximation for each power. Give the maximum number of decimal places that your calculator displays. $$\left(\frac{1}{2}\right)^{\sqrt{2}}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log \left(-\frac{1}{2} x\right)$$

For each statement, write an equivalent statement in exponential form. Do not use a calculator. $$\log _{4} \frac{1}{64}=-3$$

Solve each exponential equation. Express the solution set so that (a) solutions are in exact form and, if irrational, (b) solutions are approximated to the nearest thousandth. Support your solutions by using a calculator. $$\left(\frac{1}{3}\right)^{x}=6$$

Use a calculator to find an approximation for each power. Give the maximum number of decimal places that your calculator displays. $$.\left(\frac{1}{3}\right)^{\sqrt{6}}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\ln \left(x^{2}+7\right)$$

For each statement, write an equivalent statement in exponential form. Do not use a calculator. $$\log _{10} 0.001=-3$$