91Ó°ÊÓ

Solve the equations and check your answers. $$\ln (x-9)^{4}=8$$

Solve the equations and check your answers. $$\ln (x+2)+\ln (x-2)=0$$

Solve the exponential equation algebraically, using logarithms. $$5^{3 x}=786$$

Solve the exponential equation algebraically, using logarithms. $$8^{0.2 x}=98.6$$

Solve the exponential equation algebraically, using logarithms. $$0.8^{0.4 x}=2001$$

Solve the exponential equation algebraically, using logarithms. $$6^{-5 x}=0.007$$

Solve the equations and check your answer. $$3 e^{x-4}+5=10$$

Solve the equations and check your answer. $$2 e^{2 x}+5 e^{x}-3=0$$

Solve the equations and check your answer. $$5 \cdot 2^{2 x}-3 \cdot 2^{x}-2=0$$

Compound Interest Problem 2: If you invest \(\$ 10,000\) in a savings account that pays interest at the rate of \(7 \%\) APR (annual percentage rate), then the amount \(M\) in the account after \(x\) years is given by the exponential function \(M=10,000 \times 1.07^{x}\) a. Make a table of values of \(M\) for each year from 0 to 6 years. b. How can you conclude that the values in the table have the add-multiply property? c. Suppose that you want to cash in the savings account when the amount \(M\) reaches \(\$ 27,000 .\) Set \(M=27,000\) and solve the resulting exponential equation algebraically using logarithms. Convert the answer to months, and round appropriately to find how many whole months must elapse before \(M\) first exceeds \(\$ 27,000\)