1 > 2 1 > 2 !

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1 10 > 1 100 \frac {1}{10} > \frac {1}{100}
l n 1 10 > l n 1 100 ln \frac {1}{10} > ln \frac {1}{100}
l n 1 10 > l n ( 1 10 ) 2 ln \frac {1}{10} > ln (\frac {1}{10})^2
l n 1 10 > 2 l n ( 1 10 ) ln \frac {1}{10} > 2 \cdot ln (\frac {1}{10})

Cancelling l n ( 1 10 ) ln(\frac {1}{10}) , we obtain 1 > 2 1 > 2

What option explains the mistake?

l n ( 1 10 ) ln(\frac {1}{10}) is negative l n ( 1 10 ) ln(\frac {1}{10}) can't be canceled l n ( 1 10 ) ln(\frac {1}{10}) is zero All options are true

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1 solution

Kirsten Gouria
Feb 25, 2014

logarithm of any number less than 1 is negative!

The answer is not correct (or the options are misleading) e.g. -5 > -6
you can't remove -ve sign because this will lead to 5 > 6

my answer was you can not cancel (ln n) in this case >>>

Ossama Ismail - 7 years, 3 months ago

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yup the options are a bit confusing but on thinking we get that because ln(.1) is negative we cannot cancel it without changing the sign of the inequality. we can understand this as "ln(.1) being negative is the cause of this cancelling" Yeah i know its confusing but can't explain it here just by typing

Pranjal Rajawat - 7 years, 3 months ago

You are damn right!!

Tanya Gupta - 7 years, 3 months ago

If you do cancel the ln from both sides, the inequality sign must be flipped, because you are dividing by a negative. Thus, the result would be 2 > 1

Nanayaranaraknas Vahdam - 7 years, 2 months ago

Dividing both sides of the inequality by a negative number changes the inequality symbol to its opposite.

Isaac Lu - 7 years, 3 months ago

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