91Ó°ÊÓ

For the given functions \(f\)and \(\mathrm{g}\), find: (a) \((f \circ g)\) (4) (b) \((g \circ f)(2)\) (c) \((f \circ f)(1)\) (d) \((g \circ g)\) (0) \(f(x)=|x-2| ; \quad g(x)=\frac{3}{x^{2}+2}\)

Change each logarithmic statement to an equivalent statement involving an exponent. $$ \log _{3}\left(\frac{1}{9}\right)=-2 $$

Use properties of logarithms to find the exact value of each expression. Do not use a calculator. \(\log _{6} 9+\log _{6} 4\)

Determine whether the function is one-to-one. $$ \\{(1,2),(2,8),(3,18),(4,32)\\} $$

Find the principal needed now to get each amount, that is, find the present value. Toget \(\$ 300\) after 4 years at \(3 \%\) compounded daily

Use properties of logarithms to find the exact value of each expression. Do not use a calculator. \(\log _{5} 35-\log _{5} 7\)

For the given functions \(f\)and \(\mathrm{g}\), find: (a) \((f \circ g)\) (4) (b) \((g \circ f)(2)\) (c) \((f \circ f)(1)\) (d) \((g \circ g)\) (0) \(f(x)=\frac{3}{x+1}, \quad g(x)=\sqrt[3]{x}\)

After the release of radioactive material into the atmosphere from a nuclear power plant at Chernobyl (Ukraine) in \(1986,\) the hay in Austria was contaminated by iodine 131 (half-life 8 days). If it is safe to feed the hay to cows when \(10 \%\) of the iodine 131 remains, how long did the farmers need to wait to use this hay?

Change each logarithmic statement to an equivalent statement involving an exponent. $$ \log _{a} 3=6 $$

Solve each logarithmic equation. Express irrational solutions in exact form. $$ \log x+\log (x+15)=2 $$