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Magazine Problem 66
Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\log _{3}\left(3^{2} \cdot 4^{2}\right)\)
Problem 67
Radioactive Decay Strontium-90 has a half-life of \(29.1\) years. The amount \(S\) of 100 kilograms of strontium-90 present after \(t\) years is given by \(S=100 e^{-0.0238 t}\) How much of the 100 kilograms will remain after 50 years?
Problem 67
Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\log _{3} 4 n\)
Problem 67
Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\log _{10} 2 x=7\)
Problem 67
Find the domain, vertical asymptote, and \(x\) -intercept of the logarithmic function. Then sketch its graph.\(h(x)=\log _{2}(x+4)\)
Problem 68
Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\log _{10} 3 z=2\)
Problem 68
Radioactive Decay Neptunium-237 has a half-life of 2.1 million years. The amount \(N\) of 200 kilograms of neptunium- 237 present after \(t\) years is given by \(N=200 e^{-0.00000033007 t}\) How much of the 200 kilograms will remain after 20,000 years?
Problem 68
Find the domain, vertical asymptote, and \(x\) -intercept of the logarithmic function. Then sketch its graph.\(f(x)=\log _{4}(x-3)\)
Problem 68
Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\log _{6} 6 x\)
Problem 69
Find the domain, vertical asymptote, and \(x\) -intercept of the logarithmic function. Then sketch its graph.\(f(x)=-\log _{2} x\)
