Hey guys just wanted to get some feedback on this answer I got for this problem. My solutions don't really make sense with the context of the word problem so I'm wondering if I've done something incorrect.

Problem:

1.

$\displaystyle \log_{2}1$

$\displaystyle = \log_{2}(2^0)$

$\displaystyle = 0$

2.

$\displaystyle \log_{2}10 000$

$\displaystyle =\log_{2}10^4$

$\displaystyle =\log_{2}(2^{10/3})^4$

$\displaystyle =\log_{2}(2^{40/3})$

$\displaystyle =40/3$

Thanks for checkin!