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\(a^log_ab=b\)

 

a^log_ab=b

Saw it in a textbook (Revision) How does it work ? 

 Sep 16, 2019
 #1
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a^ ( loga b)    = b      (1)

 

I'll admit that when I first saw this in Algebra it was a little tough to see

 

Let's prove this is true :

 

Take the log of both sides

 

log a ^ (loga b)   = log b        and by a log property we have

 

( loga b) * log a  = log b        divide both sides by log a

 

loga b    = log b /log a         by the change-of-base rule for logs we can write

 

log b / log a   = log b  / log a

 

Since this is an identity....then so is  (1)

 

 

cool cool cool

 Sep 16, 2019
edited by CPhill  Sep 16, 2019

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