91Ó°ÊÓ

Write each expression as a single logarithm. $$3 \log u-\log 2 v-\log z$$

Explain the mistake that is made. The city of San Antonio, Texas, has a population that is growing at \(5 \%\) a year, compounding continuously. If there were 1.3 million people in the greater San Antonio area in \(2006,\) approximately how many people will there be in \(2016 ?\) Apply the formula \(N=N_{0} e^{\pi},\) where \(N\) represents the number of people. Solution: Use the population growth model. \(N=N_{0} e^{r t}\). Let \(N_{0}=1.3, r=5,\) and \(t=10\) \(N=1.3 e^{(5)(10)}\). Approximate with a calculator. \(6.7 \times 10^{21}\). This is incorrect. What mistake was made?

Solve the logarithmic equations exactly. $$\ln x^{2}-\ln 9=0$$

Write each expression as a single logarithm. $$\ln (x+1)+\ln (x-1)-2 \ln \left(x^{2}+3\right)$$

Determine whether each statement is true or false. When a species gets placed on an endangered species list, the species begins to grow rapidly, and then reaches a carrying capacity. This can be modeled by logistic growth.

Graph the exponential function using transformations. State the \(y\) -intercept, two additional points, the domain, the range, and the horizontal asymptote. $$f(x)=1+\left(\frac{1}{2}\right)^{x-2}$$

Evaluate the logarithms exactly (if possible). $$\ln (-1)$$

Solve the logarithmic equations exactly. $$\log x^{2}+\log x=3$$

Write each expression as a single logarithm. $$\ln \sqrt{x-1}+\ln \sqrt{x+1}-2 \ln \left(x^{2}-1\right)$$

Graph the exponential function using transformations. State the \(y\) -intercept, two additional points, the domain, the range, and the horizontal asymptote. $$f(x)=2-\left(\frac{1}{3}\right)^{x+1}$$