91Ó°ÊÓ

The number \(n\) of monthly payments of \(P\) dollars each required to pay off a loan of \(A\) dollars in its entirety at interest rate \(r\) is given by $$n=-\frac{\log \left(1-\frac{A r}{12 P}\right)}{\log \left(1+\frac{r}{12}\right)}$$ a. A college student wants to buy a car and realizes that he can only afford payments of \(\$ 200\) per month. If he borrows \(\$ 3000\) and pays it off at \(6 \%\) interest, how many months will it take him to retire the loan? Round to the nearest month. b. Determine the number of monthly payments of \(\$ 611.09\) that would be required to pay off a home loan of \(\$ 128,000\) at \(4 \%\) interest.

Solve the equation. \(\frac{e^{x}-9 e^{-x}}{2}=4\)

Solve the equation. \((\ln x)^{2}-\ln x^{5}=-4\)

Use a calculator to approximate the given logarithms to 4 decimal places. a. Avogadro's number is \(6.022 \times 10^{23}\). Approximate \(\log \left(6.022 \times 10^{23}\right)\) b. Planck's constant is \(6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{sec}\). Approximate \(\log \left(6.626 \times 10^{-34}\right)\) c. Compare the value of the common logarithm to the power of 10 used in scientific notation.

Solve the equation. \((\ln x)^{2}+\ln x^{3}=-2\)

Use a calculator to approximate the given logarithms to 4 decimal places. a. The speed of light is \(2.9979 \times 10^{8} \mathrm{~m} / \mathrm{sec}\). Approximate \(\log \left(2.9979 \times 10^{8}\right)\) b. An elementary charge is \(1.602 \times 10^{-19} \mathrm{C}\). Approximate \(\log \left(1.602 \times 10^{-19}\right)\) c. Compare the value of the common logarithm to the power of 10 used in scientific notation.

A logarithmic function \(y=\log _{b} x\) with base \(b>1\) increases over its domain. However, the rate of increase decreases with larger and larger values of \(x .\) For Exercises \(119-120\), demonstrate this statement by finding the average rate of change on each interval \([a, b] .\) Round to 4 decimal places where necessary. \(\mathrm{Y}_{1}=\log x\) a. [0.5,1] b. [1,10] c. [10,20] d. [20,30]

Solve the equation. \((\log x)^{2}=\log x^{2}\)

Solve the equation. \((\log x)^{2}=\log x^{3}\)

A logarithmic function \(y=\log _{b} x\) with base \(b>1\) increases over its domain. However, the rate of increase decreases with larger and larger values of \(x .\) For Exercises \(119-120\), demonstrate this statement by finding the average rate of change on each interval \([a, b] .\) Round to 4 decimal places where necessary. \(\mathrm{Y}_{1}=\ln x\) a. [0.5,1] b. [1,10] c. [10,20] d. [20,30]