Question 599291
The key is to express {{{ 3 }}} as a log to the base {{{ 2 }}}
{{{ log( 2, x ) = 3 }}}
{{{ log( 2, 8 ) = 3 }}}
{{{ log( 2, x-5 ) - log( 2, x+2 ) = log( 2, 8 ) }}}
Use the rule:
{{{ log(a) - log(b) = log(a/b) }}}
{{{ log( 2, ( x-5 )/( x+2 ) ) = log( 2,8 ) }}}
{{{ ( x-5 ) / ( x+2 ) = 8 }}}
{{{ x - 5 = 8*( x + 2 ) }}}
{{{ x - 5 = 8x + 16 }}}
{{{ 7x = -21 }}}
{{{ x = -3 }}}
check:
{{{ log (2, (x-5)) - log (2,(x+2) ) = 3 }}}
{{{ log (2,(-8) ) - log (2,(-1) ) = 3 }}}
{{{ log( 2, (-8)/(-1) ) = 3 }}}
{{{ log( 2,8 ) = 3 }}}
OK