Find the domain of the function. \[ g(x)=\log _{2}\left(\frac{x-8}{x}\right) \] The domain is (Type your answer in interval notation.)

Simplify \( \frac{8}{\sqrt{6}+2} \)

The half-life of radium is 1690 years. If 40 grams are present now, how much will be present in 860 years? \( \square \) grams (Do not round until the final answer. Then round to the nearest thousandth as needed.)

Write expression \( \log \left(\frac{x^{4} y^{17}}{z^{2}}\right) \) as a sum or difference of logarithms with no exponents. Simplify your answer completely. \( \log \left(\frac{x^{4} y^{17}}{z^{2}}\right)=\square \)

11. Вычислите: \( \frac{10^{7}}{5^{6} \cdot 2^{7}} \)

\#5. The ratio of pink roses to yellow roses in a flower arrangement is \( 5: 3 \). If there are 15 yellow roses, then how many total flowers are in the arrangement?