Question 1168698

given:

{{{x^a  = k }}}  → {{{log( x)  =  log (k) / a}}}

{{{y^b  = k }}}  → {{{log (y)  =  log (k )/ b}}}

{{{x^c  = t }}}  

{{{y^d  = t}}}

So 

{{{k*t= x^a*x^c = y^b*y^d = x^(a + c) = y^(b + d)}}}

then
 
{{{(a + c) log (x)  =  ( b + d) log( y)}}}

{{{(a + c)(log( k)/a)  =  (b + d)(log(k)/b)}}}


{{{(a + c)b  =  ( b + d)a}}}

{{{ab + bc  =   ab + ad}}}

[ {{{bc   =  ad }}}]  →  [ {{{ad   =  bc }}}]

answer: B) {{{ad=bc}}}