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Magazine Problem 84
Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\log _{3}(x+8)=\log _{3}(3 x+2)\)
Problem 84
Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\ln \sqrt{\frac{x^{2}}{y^{3}}}\)
Problem 85
Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\log _{10}(x+4)-\log _{10} x=\log _{10}(x+2)\)
Problem 85
Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\ln \sqrt[4]{x^{3}\left(x^{2}+3\right)}\)
Problem 86
A principal \(P\), invested at \(4.85 \%\) interest and compounded continuously, increases to an amount that is \(K\) times the principal after \(t\) years, where \(t\) is given by \(t=\frac{\ln K}{0.0485}\) Use a graphing utility to graph this function.
Problem 86
Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\log _{10} x+\log _{10}(x+1)=\log _{10}(x+3)\)
Problem 86
Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\ln \sqrt{x^{2}(x+2)}\)
Problem 87
Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\log _{4} x-\log _{4}(x-1)=\frac{1}{2}\)
Problem 87
In Exercises \(87-102\), condense the expression to the logarithm of a single quantity.\(\log _{3} x+\log _{3} 5\)
Problem 88
Condense the expression to the logarithm of a single quantity.\(\log _{5} y+\log _{5} x\)
