SOLUTION: prove that log 2 base 10 greater that 0.3

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Question 970399: prove that log 2 base 10 greater that 0.3
Found 2 solutions by lwsshak3, n2:
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
prove that log 2 base 10 greater that 0.3
exponential form of log 2 base 10 : base(10) raised to log of number(x)=number(2)
10^x=2
xlog10=log2
x=log2=.30103>0.3

Answer by n2(91) About Me  (Show Source):
You can put this solution on YOUR website!
.
prove that log 2 base 10 highlight%28highlight%28is%29%29 greater highlight%28cross%28that%29%29 than 0.3.
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            There is a proof of striking beauty.


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

Rewrite it in the form     2%5E10 > 10%5E3.

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

Divide both sides by   10:     log(2) > 3%2F10,   or     log(2) > 0.3.


Thus the statement is proven.