Symbiosis National Aptitude Test SNAP 2015 Paper

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Question : 24 of 150

Marks: +1, -0

What is the value of

(\log_{1/2} 2)(\log_{1/3} 3)(\log_{1/4}4)

....

(\log_{1/{1000}} 1000)

?

1
- 1
1 or - 1
0

Solution:

(\log_{1/2} 2)(\log_{1/3} 3)(\log_{1/4}4)

....

(\log_{1/{1000}} 1000)

=

({\log2}/{\log 1/2})({\log 3}/{\log 1/3})({\log 4}/{\log 1/4})

...

({\log1000}/{\log(1/{1000})})

(\Since \log_b a = {\log a}/{\log b})

=

({\log2}/{-\log2})({\log3}/{-\log3})({\log4}/{-\log4})

....

({\log 1000}/{-\log1000})

= (-1) × (-1) × (-1) × ..... × (-1)
(Since number of factors is odd)
= –1

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