91Ó°ÊÓ

Determine whether the statement is true or false. Justify your answer. You can determine the graph of \(f(x)=\log _{6} x\) by graphing \(g(x)=6^{x}\) and reflecting it about the \(x\) -axis.

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln x-\ln (x+1)=2$$

Prove that \(\log _{b} u^{n}=n \log _{b} u\).

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln x+\ln (x+1)=1$$

Determine whether the statement is true or false. Justify your answer. The graph of \(f(x)=\log _{3} x\) contains the point (27,3) .

A classmate claims that the following are true. (a) \(\ln (u+v)=\ln u+\ln v=\ln (u v)\) (b) \(\ln (u-v)=\ln u-\ln v=\ln \frac{u}{v}\) (c) \((\ln u)^{n}=n(\ln u)=\ln u^{n}\) Discuss how you would demonstrate that these claims are not true.

Determine whether the statement is true or false given that \(f(x)=\ln x\). Justify your answer. $$f(0)=0$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\ln x+\ln (x-2)=1$$

In Exercises \(101-104,\) sketch the graphs of \(f\) and \(g\) and describe the relationship between the graphs of \(f\) and \(g\). What is the relationship between the functions \(f\) and \(g\) ? $$f(x)=3^{x}, \quad g(x)=\log _{3} x$$

Sketch the graphs of \(f\) and \(g\) and describe the relationship between the graphs of \(f\) and \(g\). What is the relationship between the functions \(f\) and \(g\) ? $$f(x)=5^{x}, \quad g(x)=\log _{5} x$$