91Ó°ÊÓ

Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\ln (x+5)=\ln (x-1)-\ln (x+1)\)

Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\ln \frac{z}{\sqrt[3]{z+3}}\)

The population of a town will double in \(t=\frac{8 \ln 3}{\ln 63-\ln 45}\) years. Find \(t\).

The work \(W\) (in foot-pounds) done in compressing a volume of 9 cubic feet at a pressure of 15 pounds per square inch to a volume of 3 cubic feet is \(W=19,440(\ln 9-\ln 3)\). Find \(W\)

Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\ln (x+1)-\ln (x-2)=\ln x$$\ln (x+1)-\ln (x-2)=\ln x\)

Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\log _{9} \frac{\sqrt{y}}{z^{2}}\)

Students in a mathematics class were given an exam and then retested monthly with an equivalent exam. The average score \(g\) for the class can be approximated by the human memory model \(g(t)=78-14 \log _{10}(t+1), \quad 0 \leq t \leq 12\) where \(t\) is the time (in months). (a) What was the average score on the original exam? (b) What was the average score after 4 months? (c) When did the average score drop below 70 ?

Solve the logarithmic equation algebraically. Approximate the result to three decimal places.\(\log _{2}(2 x-3)=\log _{2}(x+4)\)

Use the properties of logarithms to expand the expression as a sum, difference, and/or multiple of logarithms. (Assume all variables are positive.)\(\ln \sqrt[3]{\frac{x}{y}}\)

Students in a seventh-grade class were given an exam. During the next 2 years, the same students were retested several times. The average score \(g\) can be approximated by the model \(g(t)=87-16 \log _{10}(t+1), \quad 0 \leq t \leq 24\) where \(t\) is the time (in months). (a) What was the average score on the original exam? (b) What was the average score after 6 months? (c) When did the average score drop below \(70 ?\)