Question 1089580
Say {{{ X = log(a,(b)) }}}

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Raise a to both sides:
{{{ a^X = a^(log(a,(b))) }}}
The right hand side is just b:
{{{ a^X = b }}}
Now take log base b of both sides:
{{{ log(b,(a^X)) = log(b,(b)) }}}
The left hand side is {{{ X*log(b,(a)) }}}  while the right hand side is 1:
{{{  X*log(b,(a)) = 1 }}}  —> {{{ log(b,(a))*X = 1 }}}
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Finally, since {{{ X = log(a,(b)) }}}, the proof  is completed by substituting for X:

{{{ highlight( log(b,(a))*log(a,(b)) = 1) }}}