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Prove that log_a b = 1/(log_b a)
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The relation `log_a b = 1/(log_b a)` has to be proved.
Let `X = log_a b`
=> `b = a^X`
Take the logarithm with base b of both the sides,
`log_b b = log_b(a^X)`
Use the property `log_b b = 1` and `log a^b = b*log a`
=> `1 = X*log_b a`
=> `X = 1/(log_ b a)`
But `X = log_a b` , which gives `log_a b = 1/(log_b a)`
This proves that `log_a b = 1/(log_b a)`
Posted by justaguide on September 3, 2013 at 5:57 PM (Answer #1)
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