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.)

Simplify the logarithmic expression: \( \text{\log}_{2}(8) + \text{\log}_{2}(4) \)

Julie swam, biked, and ran in a 22.2 mile triathlon. She completed the race in 2.15 hours. The function \( m=13.8 \mathrm{~h} \) represents the miles \( m \) Julie biked in \( h \) hours. Was her average speed biking less than or greater than her average speed for the entire race? Justify your answer. Round to the nearest tenth if necessary.

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. \( \log \left(\frac{x^{4} y^{17}}{z^{2}}\right)=\square \)

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

Write the expression as a sum and/or difference of logarithms. Express powers as factors. \[ \log _{2}\left(\frac{x^{10}}{x-8}\right), x>8 \] \( \log _{2}\left(\frac{x^{10}}{x-8}\right)=\square \) (Simplify your answer.)