91Ó°ÊÓ

Sketch the graph of \(f(x)=\left(\frac{1}{3}\right)^{x}\). Then refer to it and use earlier techniques to graph each finction. $$f(x)=\left(\frac{1}{3}\right)^{x}+4$$

In each of the following. (a) explain how the graph of the given finction can be obtained from the graph of \(g(x)=\log _{2} x,\) and (b) graph the function. $$f(x)=\log _{2}(x+4)$$

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\log _{6}(2 x+4)=2$$

Use the definition of inverse functions to show analytically that \(f\) and \(g\) are inverses. $$f(x)=x^{3}+4, \quad g(x)=\sqrt[3]{x-4}$$

Evaluate each expression. Do not use a calculator. $$\ln e^{2 / 3}$$

Solve each logarithmic equation. Express all solutions in exact form. Support your solutions by using a calculator. $$\log _{5}(8-3 x)=3$$

Use the definition of inverse functions to show analytically that \(f\) and \(g\) are inverses. $$f(x)=x^{3}-7, \quad g(x)=\sqrt[3]{x+7}$$

In each of the following. (a) explain how the graph of the given finction can be obtained from the graph of \(g(x)=\log _{2} x,\) and (b) graph the function. $$f(x)=\log _{2}(x-6)$$

Evaluate each expression. Do not use a calculator. $$\ln e^{x}$$

In each of the following. (a) explain how the graph of the given finction can be obtained from the graph of \(g(x)=\log _{2} x,\) and (b) graph the function. $$f(x)=3 \log _{2} x+1$$