91Ó°ÊÓ

Add or subtract as indicated. See Section 6.2. $$ \frac{m^{2}}{m+1}-\frac{1}{m+1} $$

Graph each function by finding ordered pair solutions, plotting the solutions, and then drawing a smooth curve through the plotted points. $$ f(x)=\log (x+2) $$

Solve. See the Concept Check in this section. Let \(f(x)=\log _{5} x .\) Then \(g(x)=5^{x}\) is the inverse of \(f(x)\) The ordered pair \((2,25)\) is a solution of the function \(g(x)\). a. Write this solution using function notation. b. Write an ordered pair that we know to be a solution of \(f(x)\) c. Use the answer to part b and write the solution using function notation.

Graph each function by finding ordered pair solutions, plotting the solutions, and then drawing a smooth curve through the plotted points. $$ f(x)=\log (x-2) $$

Graph each function by finding ordered pair solutions, plotting the solutions, and then drawing a smooth curve through the plotted points. $$ f(x)=\ln x-3 $$

Explain why negative numbers are not included as logarithmic bases.

Explain why 1 is not included as a logarithmic base.

Graph each function by finding ordered pair solutions, plotting the solutions, and then drawing a smooth curve through the plotted points. $$ f(x)=\ln x+3 $$

Graph each function by finding ordered pair solutions, plotting the solutions, and then drawing a smooth curve through the plotted points. Graph \(f(x)=e^{x}(\text { Exercise } 79), f(x)=e^{x}+2(\text { Exercise } 83)\) and \(f(x)=e^{x}-3(\text { Exercise } 84)\) on the same screen. Discuss any trends shown on the graphs.

Solve by first writing as an exponent. $$ \log _{7}(5 x-2)=1 $$