Question 1118244
{{{10^2}}} versus  {{{2^10}}}



What if both were to be in base 2?


{{{2^p=10^2}}}
{{{log(2,2^p)=log(2,10^2)}}}
{{{p*1=2*log(2,10)}}}


{{{2^(2*log(2,10))}}} versus {{{2^10}}}


Compare  {{{2*log(2,10)}}} with  {{{10}}}.


Note that 2^3=8 and 2^4=16  so {{{3<log(2,10)<4}}}.

Knowing that log(2,10)<=4, setup the inequality  {{{2*4<10}}}.



{{{2*log(2,10)<10}}}
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{{{10^2<2^10}}}