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

 Sep 16, 2019

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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