91Ó°ÊÓ

Solving an Equation In Exercises 19-24, solve for \(x\) or \(b\) . $$ \begin{array}{l}{\text { (a) } \log _{10} 1000=x} \\ {\text { (b) } \log _{10} 0.1=x}\end{array} $$

Use a graphing utility to graph the function. Then use the Horizontal Line Test to determine whether the function is one-to-one on its entire domain and therefore has an inverse function. \(f(x)=5 x \sqrt{x-1}\)

Finding an Indefinite Integral In Exercises \(1-20\) , find the indefinite integral. $$ \int \frac{x-2}{(x+1)^{2}+4} d x $$

In Exercises 17–22, find the limit. $$ \lim _{x \rightarrow-\infty} \operatorname{csch} x $$

Finding an Indefinite Integral In Exercises \(1-26,\) find the indefinite integral.. $$ \int \frac{x^{3}-4 x^{2}-4 x+20}{x^{2}-5} d x $$

In Exercises 19–28, use the properties of logarithms to expand the logarithmic expression. $$ \ln \sqrt{x^{5}} $$

Sketching a Graph In Exercises \(17-22,\) sketch the graph of the function. $$ y=e^{x-1} $$

Solving an Equation In Exercises 19-24, solve for \(x\) or \(b\) . $$ \begin{array}{l}{\text { (a) } \log _{3} \frac{1}{81}=x} \\ {\text { (b) } \log _{6} 36=x}\end{array} $$

Use a graphing utility to graph the function. Then use the Horizontal Line Test to determine whether the function is one-to-one on its entire domain and therefore has an inverse function. \(g(x)=(x+5)^{3}\)

Solving an Equation In Exercises 19-24, solve for \(x\) or \(b\) . $$ \begin{array}{l}{\text { (a) } \log _{3} x=-1} \\ {\text { (b) } \log _{2} x=-4}\end{array} $$