The value of the expression \frac{1}{1+\log _{u} v w}+\frac{1}{1+\log _{u} w u}+\frac{1}{1+\log _{u} u v} is

GATE Mechanical Engineering (ME) 2018 Shift 2 Solved Paper

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The value of the expression

\;{1}/{1+\log _{u} v w}+\;{1}/{1+\log _{u} w u}+\;{1}/{1+\log _{u} u v}

Solution:

\;{1}/{1+\log _{u} v w}+\;{1}/{1+\log _{v} w u}+\;{1}/{1+\log _{w} u v}

\;{1}/{\log _{u} u+\log _{u} w v}+\;{1}/{\log _{v} v+\log _{v} u w}+\;{1}/{\log _{w} w+\log _{w} u v}

\;{1}/{\log _{u} u v w}+\;{1}/{\log _{v} u v w}+\;{1}/{\log _{w} u v w}

\log _{u v w} u+\log _{u v w} v+\log _{u v w} w

\log _{u v w} u v w

=1

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