Latest Elitmus Aptitude Question SOLUTION: log2002 base n -> log2002 base n find the value of log22002 + log32002 + log42002 + log52002 - log102002 - log112002 - log122002 - log132002 - log142002 Option a) 0 b) 1 c) -1 d)

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(#M40032531) ELITMUS Numerical Ability question Logarithmic Problem Keep an EYE

log2002 base n -> log2002 base n
find the value of
log22002 + log32002 + log42002 + log52002 - log102002 - log112002 - log122002 - log132002 - log142002
Option
a) 0
b) 1
c) -1
d) 2002log2002

Asked In Elitmus (10 years ago)

Unsolved Read Solution (4)

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Read Solution (4) :

Arvid kumar  (10 years ago)

log a base b
logba=loga/logb
so
log2 2002+log3 2002 +...-(log10 2002+log11 2002+...)
log2002/log2 + log2002/log3+... -(log2002/log10 + log2002/log11 +...)
log2002 ((1/log2 + 1/log3+...)-(1/log10 + 1/log11 +...))
log2002 (((log2)^-1 + (log3)^-1 + ...) - ((log10)^-1 + (log11)^-1 + ...))
log2002 ((-log1 - log2 - ...)-(-log10 -log11 -....))
log2002 ((log10 + log 11 + ...)-(log2+log3+...))
log2002 (log ((10*11*12*13*14)/(2*3*4*5))
log2002 (log2002)
log2002/(log2002)^-1
-log2002/log2002
-1 ANS

Is this solution Helpfull? Yes (34) | No (10)  

T.VIGNESWARA REDDY  (9 years ago)

log a base b means loga/logb so if we do this log(2*3*4*5/10*11*12*13*14) all log 2002 cancelled out so log(01/11*13*14) is negative so ans is -1

Is this solution Helpfull? Yes (2) | No (2)  

Mithilesh Times  (8 years ago)

Ans -1 is correct.

Is this solution Helpfull? Yes (1) | No   

Asgar Pasha  (9 years ago)

on solving you finally get (log 2002)(log 2002)=(log 2002)^2 which is somewhere between 9 and 15 which is not found in any of the options.Hence either the question is wrong or the options are inappropriate......

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