91Ó°ÊÓ

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

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

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

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

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. \(-2\)

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. $$f(x)=\log _{4}\left(x^{2}-4 x-21\right)$$

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

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

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