91Ó°ÊÓ

In Exercises \(59-66,\) approximate the logarithm using the properties of logarithms, given \(\log _{b} 2 \approx 0.3562, \log _{b} 3 \approx 0.5646,\) and \(\log _{b} 5 \approx 0.8271\). $$\log _{b} \frac{2}{3}$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{2} x+\log _{2}(x+2)=\log _{2}(x+6)$$

Function \(\quad\) Value $$ g(x)=-\ln x \quad x=\frac{1}{2}$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log _{4} x-\log _{4}(x-1)=\frac{1}{2}$$

Evaluate \(g(x)=\ln x\) at the indicated value of \(x\) without using a calculator. $$x=e^{5}$$

Complete the table to determine the balance \(A\) for \(\$ 12,000\) invested at rate \(r\) for \(t\) years, compounded continuously. $$\begin{array}{|l|l|l|l|l|l|} \hline t & 10 & 20 & 30 & 40 & 50 \\ \hline A & & & & & \\ \hline \end{array}$$ $$r=6.5 \%$$

Determine whether the statement is true or false. Justify your answer. The domain of a logistic growth function cannot be the set of real numbers.

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$\log 8 x-\log (1+\sqrt{x})=2$$

Evaluate \(g(x)=\ln x\) at the indicated value of \(x\) without using a calculator. $$x=e^{-4}$$

In Exercises \(59-66,\) approximate the logarithm using the properties of logarithms, given \(\log _{b} 2 \approx 0.3562, \log _{b} 3 \approx 0.5646,\) and \(\log _{b} 5 \approx 0.8271\). $$\log _{b} \sqrt{2}$$