<PRE><B>Question 994910</B>
.
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. &amp;nbsp;{{{(81/16)^(-3/4)}}}.


Calculate &amp;nbsp;{{{(81/16)^(1/4)}}} &amp;nbsp;first. &amp;nbsp;It is {{{3/2}}}.


Then calculate &amp;nbsp;{{{(3/2)^(-1)}}}. &amp;nbsp;It is &amp;nbsp;{{{2/3}}}.


Finally, &amp;nbsp;calculate &amp;nbsp;{{{(2/3)^3}}}. &amp;nbsp;It is &amp;nbsp;{{{(8/27)}}}. &amp;nbsp;This is your answer.



2. &amp;nbsp;{{{10^log(10,3)}}} = 3.


It is so due to the definition of the logarithm.


It is one of basic properties of the logarithm: &amp;nbsp;{{{a^log(a,N)}}} = N.



3. {{{log(10,100))}}} + {{{log(e, (sqrt(e)))}}}.


If I correctly read this, &amp;nbsp;it is &amp;nbsp;{{{2}}} + {{{1/2}}} = {{{2}}}{{{1/2}}}.


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