Question 994910
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Find numerical values without using a calculator:
(81/16) to the power -3/4
10 to the power log3
Log 100 + ln (square root e)
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1.  {{{(81/16)^(-3/4)}}}.


Calculate  {{{(81/16)^(1/4)}}}  first.  It is {{{3/2}}}.


Then calculate  {{{(3/2)^(-1)}}}.  It is  {{{2/3}}}.


Finally,  calculate  {{{(2/3)^3}}}.  It is  {{{(8/27)}}}.  This is your answer.



2.  {{{10^log(10,3)}}} = 3.


It is so due to the definition of the logarithm.


It is one of basic properties of the logarithm:  {{{a^log(a,N)}}} = N.



3. {{{log(10,100))}}} + {{{log(e, (sqrt(e)))}}}.


If I correctly read this,  it is  {{{2}}} + {{{1/2}}} = {{{2}}}{{{1/2}}}.