SOLUTION: 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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Question 994910: 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)
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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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.  %2881%2F16%29%5E%28-3%2F4%29.

Calculate  %2881%2F16%29%5E%281%2F4%29  first.  It is 3%2F2.

Then calculate  %283%2F2%29%5E%28-1%29.  It is  2%2F3.

Finally,  calculate  %282%2F3%29%5E3.  It is  %288%2F27%29.  This is your answer.


2.  10%5Elog%2810%2C3%29 = 3.

It is so due to the definition of the logarithm.

It is one of basic properties of the logarithm:  a%5Elog%28a%2CN%29 = N.


3. log%2810%2C100%29%29 + log%28e%2C+%28sqrt%28e%29%29%29.

If I correctly read this,  it is  2 + 1%2F2 = 21%2F2.