Question 810861
{{{ log( 4,(b+27) ) - log( 4,(b-7) ) = log( 4,b ) }}}
{{{ log( 4, ( b + 27 ) / ( b - 7 ) ) = log( 4,b ) }}}
{{{  ( b + 27 ) / ( b - 7 ) ) = b }}}
{{{ b + 27 = b*( b - 7 ) }}}
{{{ b + 27 = b^2 - 7b }}}
{{{ b^2 - 8b - 27 = 0 }}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ( I'll use {{{x}}} instead of {{{b}}} )
{{{ a = 1 }}}
{{{ b = -8 }}}
{{{ c = -27 }}}
{{{x = (-(-8) +- sqrt( (-8)^2-4*1*(-27) ))/(2*1) }}} 
{{{x = ( 8 +- sqrt( 64 + 108 )) / 2 }}} 
{{{x = ( 8 +- sqrt( 172 )) / 2 }}} 
{{{ x = ( 8 + 2*sqrt(43) ) / 2 }}}
{{{ b =  4 + sqrt(43) }}}
and
{{{ b = 4 - sqrt(43) }}}
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