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Ashwathy Menon Grade: Upto college level
        

Q.1} 1/5 < log of 2 to the base 10 < 1/3.......................


can u tell whether this is true or false?? when i tried got the statement as false..................

8 years ago

Answers : (1)

AskIITians Expert Hari Shankar IITD
17 Points
										

Lets assume the statement is true.


log102> 1/5


logxy > z implies that y > xz


Therefore,


2 > 101/5


or 25>(101/5)5  (raising both sides to power 5)


or, 32>10, which is correct.


Now consider the other inequality.


log102< 1/3


Again, logxy > z implies that y > xz


Therefore 2 < 101/3


or, 23>(101/3)3 (raising both sides to power 3)


or, 8>10, which is not true.


Hence, log102> 1/5 is right, but  log102< 1/3 does not hold.


So 1/5 < log of 2 to the base 10 < 1/3 is False


 


 


 


 

8 years ago
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