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Magazine Problem 72
Find the logarithm using common logarithms and the change-of-base formula. $$\log _{\pi} 100$$
Problem 72
Simplify. $$e^{\ln x^{3}}$$
Problem 72
Use a graphing calculator to find the approximate solutions of the equation. $$\log _{3} x+7=4-\log _{5} x$$
Problem 73
Find the inverse by thinking about the operations of the function and then reversing, or undoing, them. Check your work algebraically. FUNCTION $$f(x)=-x$$ INVERSE $$f^{-1}(x)=$$
Problem 73
Find the logarithm using common logarithms and the change-of-base formula. $$\log _{200} 50$$
Problem 73
Salvage Value. \(\quad\) A restaurant purchased a 72 -in. range with six burners for \(\$ 6982 .\) The value of the range each year is \(85 \%\) of the value of the preceding year. After \(t\) years, its value, in dollars, is given by the exponential function \(V(t)=6982(0.85)^{t}\) a) Graph the function. b) Find the value of the range after \(0,1,2,5,\) and 8 years. c) The restaurant decides to replace the range when its value has declined to \(\$ 1000 .\) After how long will the range be replaced?
Problem 73
Simplify. $$\ln e^{8 t}$$
Problem 74
Simplify. $$\log 10^{-k}$$
Problem 74
Find the inverse by thinking about the operations of the function and then reversing, or undoing, them. Check your work algebraically. FUNCTION $$f(x)=\sqrt[3]{x}-5$$ INVERSE $$f^{-1}(x)=$$
Problem 74
Salvage Value. \(\quad\) A landscape company purchased a backhoe for \(\$ 56,395 .\) The value of the backhoe each year is \(90 \%\) of the value of the preceding year. After t years, its value, in dollars, is given by the exponential function $$ V(t)=56,395(0.9)^{t} $$ a) Graph the function. b) Find the value of the backhoe after \(0,1,3,6,\) and 10 years. Round to the nearest dollar.
