Question 1157218
{{{ log( 2, x+1 ) + log( 2, x+2 ) = log( 2, 6 ) }}}
{{{ log( 2, (x+1 )*(x+2) ) = log( 2,6 ) }}}
{{{ ( x+1 )*( x+2 ) = 6 }}}
{{{ x^2 + 3x + 2 = 6 }}}
{{{ x^2 + 3x - 4 = 0 }}}
complete the square
{{{ x^2 + 3x + ( 3/2 )^2 = ( 3/2 )^2 + 4 }}}
{{{ x^2 + 3x + 9/4 = 9/4 + 16/4 }}}
{{{ ( x + (3/2) )^2 = 25/4 }}}
{{{ ( x + (3/2) )^2 = ( 5/2 )^2 }}}
{{{ x + 3/2 = 5/2 }}}
{{{ x = 1 }}}
and
{{{ x + 3/2 = -5/2 }}}
{{{ x = -4 }}}
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check answers:
{{{ log( 2, x+1 ) + log( 2, x+2 ) = log( 2, 6 ) }}}
{{{ log( 2, 1+1 ) + log( 2, 1+2 ) = log( 2, 6 ) }}}
{{{ log( 2,2 ) + log( 2,3 ) = log( 2,6 ) }}}
{{{ log( 2, 2*3 ) = log( 2,6 ) }}}
{{{ log( 2,6 ) = log( 2,6 ) }}}
OK
I can't use the negative solution: that says that 
2 raised to some power gives a negative result-
not valid.
get a 2nd opinion if needed