SOLUTION: If N=ab, show that 1/log (base a)N + 1/log (base b)N = 1
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Question 777872
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If N=ab, show that 1/log (base a)N + 1/log (base b)N = 1
Answer by
solver91311(24713)
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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
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it