SOLUTION: If N=ab, show that 1/log (base a)N + 1/log (base b)N = 1

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Question 777872: If N=ab, show that 1/log (base a)N + 1/log (base b)N = 1

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!




Use the base changing formula:



Then make the substitution:



But since ,



Then, since the sum of the logs is the log of the product:



Which is true for all a, b in the domain of the log function.

John

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