91Ó°ÊÓ

Write each expression as a single logarithm. $$\frac{1}{2} \log _{b} x-\frac{2}{3} \log _{b} y$$

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

Evaluate the logarithms exactly (if possible). $$\log _{1 / 7} 2401$$

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

Evaluate the logarithms exactly (if possible). $$\log 0$$

Solve the logarithmic equations exactly. $$\log _{2}(4 x-1)=-3$$

Explain the mistake that is made. The city of Orlando, Florida, has a population that is growing at \(7 \%\) a year, compounding continuously. If there were 1.1 million people in greater Orlando in \(2006,\) approximately how many people will there be in \(2016 ?\) Apply the formula \(N=N_{0} e^{r t},\) where \(N\) represents the number of people. Solution: Use the population growth model. \(N=N_{0} e^{r t}\). Let \(N_{0}=1.1, r=7,\) and \(t=10 . \quad N=1.1 e^{(7)(10)}\). Approximate with a calculator. \(2.8 \times 10^{30}\). This is incorrect. What mistake was made?

Evaluate the logarithms exactly (if possible). $$\ln 0$$

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

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