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Q.1} 1/5 can u tell whether this is true or false?? when i tried got the statement as false..................

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..................

Grade:Upto college level

1 Answers

AskIITians Expert Hari Shankar IITD
17 Points
12 years ago

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

 

 

 

 

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