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) (Show Source): You can put this solution on YOUR website!
}\ +\ \frac{1}{\log_b(ab)}\ =^?\ 1)
Use the base changing formula:
\ =\ \frac{\log_a(ab)}{\log_a(b)})
Then make the substitution:
}\ +\ \frac{\log_a(b)}{\log_a(ab)}\ =^?\ 1)
But since \ =\ 1)
,
}{\log_a(ab)}\ +\ \frac{\log_a(b)}{\log_a(ab)}\ =^?\ 1)
Then, since the sum of the logs is the log of the product:
}{\log_a(ab)}\ =^?\ 1)
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
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