91Ó°ÊÓ

The Louisiana Purchase. In \(1803,\) the United States negotiated the Louisiana Purchase with France. The country doubled its territory by adding \(827,000\) square miles of land for \(\$ 15\) million. If the land appreciated at the rate of \(6 \%\) each year, what would one square mile of land be worth in \(2005 ?\)

Solve each equation. $$ \ln \left(x^{2}+4 x\right)=\ln \left(x^{2}+16\right) $$

Solve for \(x .\) See Example 3. $$ \log _{x} 9=2 $$

In Exercises 53–58, assume that there are no deposits or withdrawals. Compound Interest. An initial deposit of \(\$ 10,000\) earns \(8 \%\) interest, compounded quarterly. How much will be in the account after 10 years?

Each of the following functions is one-to-one. Find the inverse of each function and express it using \(f^{-1}(x)\) notation. $$ f(x)=\frac{x^{7}}{2} $$

Solve for \(x .\) See Example 3. $$ \log _{8} x=2 $$

Solve each equation. $$ \log x+\log (x-48)=2 $$

Use a calculator to evaluate each expression, if possible. Express all answers to four decimal places. See Using Your Calculator: Evaluating Base-e (Natural) Logarithms. $$ \ln 0.675 $$

In Exercises 53–58, assume that there are no deposits or withdrawals. Compound Interest. An initial deposit of \(\$ 10,000\) earns \(8 \%\) interest, compounded monthly. How much will be in the account after 10 years?

Solve for \(x .\) See Example 3. $$ \log _{7} x=0 $$