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If a and b are positive real numbers, show that  log_a  b= 1/ log_b  a

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roshan-rox | Valedictorian

Posted July 7, 2013 at 6:35 PM via web

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If a and b are positive real numbers, show that 

log_a  b= 1/ log_b  a

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted July 7, 2013 at 6:43 PM (Answer #1)

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Let us say;

`y = log_ab`

Now remove log from right side.

`a^y = b`

Now take log on both side with respect to base b.

`log_b(a^y) = log_bb`

`ylog_ba = 1`

`y = 1/(log_ba)`

 

We know that `y = log_ab`

`log_ab = 1/(log_ba)` answer as required.

 

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