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Magazine Problem 99
(a) use a graphing utility to graph the function, (b) find the domain, (c) use the graph to find the open intervals on which the function is increasing and decreasing, and (d) approximate any relative maximum or minimum values of the function. Round your results to three decimal places. $$f(x)=\frac{x}{2}-\ln \frac{x}{4}$$
Problem 99
Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answer(s) using a graphing utility. $$-2+2 \ln 3 x=17$$
Problem 100
(a) use a graphing utility to graph the function, (b) find the domain, (c) use the graph to find the open intervals on which the function is increasing and decreasing, and (d) approximate any relative maximum or minimum values of the function. Round your results to three decimal places. $$g(x)=6 x \ln x$$
Problem 100
Find the exact value of the logarithm without using a calculator. If this is not possible, state the reason.$$3 \ln e^{5}$$.
Problem 100
Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answer(s) using a graphing utility. $$3+2 \ln x=10$$
Problem 101
Find the exact value of the logarithm without using a calculator. If this is not possible, state the reason.$$\ln \frac{1}{\sqrt{e}}$$.
Problem 101
(a) use a graphing utility to graph the function, (b) find the domain, (c) use the graph to find the open intervals on which the function is increasing and decreasing, and (d) approximate any relative maximum or minimum values of the function. Round your results to three decimal places. $$h(x)=\frac{14 \ln x}{x}$$
Problem 102
Find the exact value of the logarithm without using a calculator. If this is not possible, state the reason.$$\ln \sqrt[5]{e^{3}}$$.
Problem 102
Solve the logarithmic equation algebraically. Round the result to three decimal places. Verify your answer(s) using a graphing utility. $$4 \log _{10}(x-6)=11$$
Problem 102
(a) use a graphing utility to graph the function, (b) find the domain, (c) use the graph to find the open intervals on which the function is increasing and decreasing, and (d) approximate any relative maximum or minimum values of the function. Round your results to three decimal places. $$f(x)=\frac{x}{\ln x}$$
