91Ó°ÊÓ

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

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

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. $$f(x)=\log \left(\frac{x+1}{x-5}\right)$$

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. $$f(x)=\left(\frac{2}{3}\right)^{x}$$

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

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

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

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. $$f(x)=e^{x}$$

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