Question 970399
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prove that log 2 base 10 {{{highlight(highlight(is))}}} greater {{{highlight(cross(that))}}} <U>than</U> 0.3.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;There is a proof of striking beauty.



Start from this inequality 1024 > 1000, which obviously is valid.


Rewrite it in the form  &nbsp;&nbsp;&nbsp;&nbsp;{{{2^10}}} > {{{10^3}}}.


Take logarithm base 10 of both sides:  &nbsp;&nbsp;&nbsp;&nbsp;10*log(2) > 3.


Divide both sides by &nbsp;&nbsp;10:  &nbsp;&nbsp;&nbsp;&nbsp;log(2) > {{{3/10}}},  &nbsp;&nbsp;or  &nbsp;&nbsp;&nbsp;&nbsp;log(2) > 0.3.



Thus the statement is proven.