NIMCET 2012 Question Paper with solutions

© examsiri.com

Question : 34 of 120

Marks: +1, -0

If x =

\log_a

bc , y =

\log_b

ca and z =

log_c

ab , then

1/{1+x}+1/{1+y}+1/{1+z}

is equal to

abc
$√{ab}+√{bc}+√{ca}$
1
x + y + z

Solution:

Given that,

x=\log _{a} b c=\;{\log b c}/{\log a}

y=\log _{b} c a=\;{\log c a}/{\log b}

and

\;\; z=\log _{c} a b=\;{\log a b}/{\log c}

∴ \;\; \;{1}/{1+x}+\;{1}/{1+y}+\;{1}/{1+z}

=\;{1}/{1+{\log b c}/{\log a}} +\;{1}/{1+\;{\log c a}/{\log b}}+\;{1}/{1+\;{\log a b}/{\log c}}

=\;{\log a}/{\log a b c}+\;{\log b}/{\log a b c}+\;{\log c}/{\log a b c}=\;{\log a b c}/{\log a b c}=1

© examsiri.com

Go to Question:

Prev Question

Next Question