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Question
If `"a" = "log""p"^2/"qr", "b" = "log""q"^2/"rp", "c" = "log""r"^2/"pq"`, find the value of a + b + c.
Solution
`"a" = "log""p"^2/"qr", "b" = "log""q"^2/"rp", "c" = "log""r"^2/"pq"`
Consider,
a + b + c
= `"log""p"^2/"qr"+ "log""q"^2/"rp"+ "log""r"^2/"pq"`
= logp2 - log qr + log q2 - logrp + logr2 - logpq
= 2logp - (logq + logr) + 2logq - (logr + logp) + 2logr - (logp + logq)
= 2logp - logq - logr + 2logq - logr - logp + 2logr - logp - logq
= 0.
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