Let \( G, O, E \) and \( L \) be positive real numbers such that
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Let \( G, O, E \) and \( L \) be positive real numbers such that
\( \log (G \cdot L)+\log (G \cdot E)=3, \log (E \cdot L)+\log (E \cdot O)=4 \),
\( \mathrm{P} \)
\( \log (O \cdot G)+\log (O \cdot L)=5 \) (base of the log is 10).
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If the minimum value of \( 3 G+2 L+2 O+E \) is \( 2^{\lambda} 3^{\mu} 5^{\nu} \),
where \( \lambda, \mu \) and \( v \) are whole numbers, the value of \( \sum\left(\lambda^{\mu}+\mu^{\lambda}\right) \) is
(a) 7
(b) 13
(c) 19
(d) None of these
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