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prove identity , loga N . logb N + logb ...

prove identity , `log_a N . log_b N + log_b N .log_c N + log_c N log_a N = (log_a N .log_b N log_c N)/(log_(abc) N)`

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Prove the following identities: (a) (log_(a) n)/(log_(ab) n) = 1+ log_(a) b" "(b) log_(ab) x = (log_(a) x log_(b) x)/(log_(a) x + log_(b) x) .

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Show that log_a N + log (1)/(a)N=0