Question 686808
{{{ ln (x-8) - ln (x+7)= ln (x-10) - ln (x+8) }}}
{{{ ln( ( x-8 ) / ( x+7 ) ) = ln( ( x-10) / ( x+8 ) ) }}}
{{{ ( x-8 ) / ( x+7 ) = ( x-10) / ( x+8 ) }}}
Multiply both sides by {{{ ( x+7 )*( x+8 ) }}}
{{{ ( x-8 )*( x+8 ) = ( x -10 )*( x+7 ) }}}
{{{ x^2 - 64 = x^2 - 10x + 7x - 70 }}}
{{{ -64 = -3x - 70 }}}
{{{ 3x = -70 + 64 }}}
{{{ 3x = -6 }}}
{{{ x = -2 }}}
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I'm doubtful that this is the right solution.
It works for
{{{ ( x-8 ) / ( x+7 ) = ( x-10) / ( x+8 ) }}}
{{{ ( -2-8 ) / ( -2+7 ) = ( -2-10) / ( -2+8 ) }}}
{{{ -10 / 5 = -12 / 6 }}}
{{{ -2 = -2 }}}
But it doesn't work for
{{{ ln (x-8) - ln (x+7)= ln (x-10) - ln (x+8) }}}
{{{ ln (-2-8) - ln (-2+7)= ln (-2-10) - ln (-2+8) }}}
{{{ ln (-10) - ln (5)= ln (-12) - ln (6) }}}
There is no log to a positive base that 
gives me {{{ -10 }}} or {{{ -12 }}}
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I would get a 2nd opinion on this one