91Ó°ÊÓ

Compound Interest Which of the given interest rates and compounding periods would provide the better investment? (a) 5\(\%\) per year, compounded semiannully (b) 5\(\%\) per year, compounded continuously

Use the definition of the logarithmic function to find \(x\). $$ \begin{array}{ll}{\text { (a) } \log _{x} 6=\frac{1}{2}} & {\text { (b) } \log _{x} 3=\frac{1}{3}}\end{array} $$

Solve the equation. \(X^{2} e^{X}+X e^{X}-e^{X}=0\)

\(19-44\) Use the Laws of Logarithms to expand the expression. $$ \ln \left(x \sqrt{\frac{y}{z}}\right) $$

(a) Sketch the graphs of \(f(x)=2^{x}\) and \(g(x)=3\left(2^{x}\right)\) (b) How are the graphs related?

Solve the logarithmic equation for \(x.\) \(\ln x=10\)

Use a calculator to evaluate the expression, correct to four decimal places. $$ \begin{array}{llll}{\text { (a) } \log 2} & {\text { (b) } \log 35.2} & {\text { (c) } \log \left(\frac{2}{3}\right)}\end{array} $$

Investment A sum of \(\$ 5000\) is invested at an interest rate of 9\(\%\) per year, compounded continuously. (a) Find the value \(A(t)\) of the investment after \(t\) years. (b) Draw a graph of \(A(t) .\) (c) Use the graph of \(A(t)\) to determine when this investment will amount to \(\$ 25,000\) .

Use a calculator to evaluate the expression, correct to four decimal places. $$ \begin{array}{llll}{\text { (a) } \log 50} & {\text { (b) } \log \sqrt{2}} & {\text { (c) } \log (3 \sqrt{2})}\end{array} $$

\(19-44\) Use the Laws of Logarithms to expand the expression. $$ \ln \frac{3 x^{2}}{(x+1)^{10}} $$