Chapter 6

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. $$0.8^{x}=4$$

Use a calculator to find an approximation for each power. Give the maximum number of decimal places that your calculator displays. $$4.1^{-\sqrt{3}}$$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\ln \left(x^{4}+8\right)$$

For each statement, write an equivalent statement in exponential form. Do not use a calculator. $$\log _{3} \sqrt[3]{9}=\frac{2}{3}$$

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. $$0.6^{x}=3$$

Use a calculator to find an approximation for each power. Give the maximum number of decimal places that your calculator displays. $$6 .4^{-\sqrt{3}}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\ln \left(-x^{2}+4\right)$$

For each statement, write an equivalent statement in exponential form. Do not use a calculator. $$\log \sqrt{10}=0.5$$

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. $$4^{x-1}=3^{2 x}$$

Use a calculator to find an approximation for each power. Give the maximum number of decimal places that your calculator displays. $$\sqrt{7} \sqrt{7}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\ln \left(-x^{2}+16\right)$$

For each statement, write an equivalent statement in exponential form. Do not use a calculator. $$\ln e^{6}=6$$

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. $$2^{x+3}=5^{x}$$

Use a calculator to find an approximation for each power. Give the maximum number of decimal places that your calculator displays. $$\sqrt{13}-\sqrt{13}$$

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

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log _{4}\left(x^{2}-4 x-21\right)$$

March the logarithm in Column I with its value in Column II. Remember that \(\log _{a} x\) is the exponent to which a must be raised in onder to obtain \(x\). \(\mathbf{I}\) (a) \(\log _{2} 16\) (b) \(\log _{3} 1\) (c) \(\log _{10} 0.1\) (d) \(\log _{2} \sqrt{2}\) (e) \(\log _{e} \frac{1}{e^{2}}\) (f) \(\log _{1 / 2} 8\) \(\mathbf{II}\) A. 0 B. \(\frac{1}{2}\) C. 4 D. \(-3\) E. \(-1\) J. \(-2\)

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. $$6^{x+1}=4^{2 x-1}$$

Decide whether each function is one-to-one. $$y=-(x+3)^{2}-8$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log _{6}\left(2 x^{2}-7 x-4\right)$$

March the logarithm in Column I with its value in Column II. Remember that \(\log _{a} x\) is the exponent to which a must be raised in onder to obtain \(x\). \(\boldsymbol{I}\) (a) \(\log _{3} 81\) (b) \(\log _{3} \frac{1}{3}\) (c) \(\log _{10} 0.01\) (d) \(\log _{6} \sqrt{6}\) (e) \(\log _{e} 1\) (f) \(\log _{3} 27^{3 / 2}\) \(\mathbf{II}\) A. \(-2\) B. \(-1\) C. 0 D. \(\frac{1}{2}\) E. \(\frac{9}{2}\) F. 4

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. $$3^{x-4}=7^{2 x+5}$$

Decide whether each function is one-to-one. $$y=2 x^{3}+1$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log \left(x^{3}-x\right)$$

Solve each equation. Give the exact answer. $$\log _{5} 125=x$$

Decide whether each function is one-to-one. $$y=-2 x^{5}-4$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log \left(x^{3}-81 x\right)$$

Solve each equation. Give the exact answer. $$\log _{3} 81=x$$

Decide whether each function is one-to-one. $$y=-\sqrt[3]{x+5}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log \left(\frac{x+3}{x-4}\right)$$

Solve each equation. Give the exact answer. $$\log _{x} 3^{12}=24$$

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. $$e^{x-3}=2^{3 x}$$

Graph each function by hand and support your sketch with a calculator graph. Give the domain, range. and equation of the asymptote. Determine if \(f\) is increasing or decreasing on its domain. $$f(x)=-1.5^{x}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log \left(\frac{x+1}{x-5}\right)$$

Decide whether each function is one-to-one. $$y=\frac{1}{x+2}$$

Solve each equation. Give the exact answer. $$\log _{x} 5^{2}=6$$

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. $$e^{a .5 x}=3^{1-2 x}$$

Graph each function by hand and support your sketch with a calculator graph. Give the domain, range. and equation of the asymptote. Determine if \(f\) is increasing or decreasing on its domain. $$f(x)=\left(\frac{2}{3}\right)^{x}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log |3 x-7|$$

Decide whether each function is one-to-one. $$y=\frac{-4}{x-8}$$

Solve each equation. Give the exact answer. $$\log _{6} x=-3$$

Graph each function by hand and support your sketch with a calculator graph. Give the domain, range. and equation of the asymptote. Determine if \(f\) is increasing or decreasing on its domain. $$f(x)=e^{x}$$

Find the domain of each logarithmic function analytically. You may wish to support your answer graphically. $$f(x)=\log |6 x+6|$$

Decide whether each function is one-to-one. $$f(x)=-7$$

Solve each equation. Give the exact answer. $$\log _{4} x=-\frac{1}{6}$$

Graph each function by hand and support your sketch with a calculator graph. Give the domain, range. and equation of the asymptote. Determine if \(f\) is increasing or decreasing on its domain. $$f(x)=-e^{x}$$

Decide whether each function is one-to-one. $$f(x)=\left\\{\begin{aligned} 3 & \text { if } x \geq 0 \\ -x & \text { if } x<0 \end{aligned}\right.$$

Solve each equation. Give the exact answer. $$\log _{x} 16=\frac{4}{3}$$

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. $$0.05(1.15)^{x}=5$$

Graph each function by hand and support your sketch with a calculator graph. Give the domain, range. and equation of the asymptote. Determine if \(f\) is increasing or decreasing on its domain. $$f(x)=e^{x+1}$$