Question 759924

{{{log(2,x+7) + log(2,x+8)=1}}}

{{{log(2,((x+7)(x+8)))=1}}}

{{{log(2,((x+7)(x+8)))=1}}}


{{{log((x+7)(x+8))/log(2)=1}}}

{{{log((x+7)(x+8))=1*log(2)}}}

{{{log((x+7)(x+8))=log(2)}}}..if log same, then

{{{(x+7)(x+8)=2}}}

{{{x^2+8x+7x+56=2}}}

{{{x^2+15x+56-2=0}}}

{{{x^2+15x+54=0}}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

{{{x = (-15 +- sqrt( 15^2-4*1*54 ))/(2*1) }}} 

{{{x = (-15 +- sqrt( 225-216 ))/2 }}} 

{{{x = (-15 +- sqrt( 9))/2 }}} 

{{{x = (-15 +- 3)/2 }}} 

solutions:

{{{x = (-15 + 3)/2 }}} 

{{{x = -12/2 }}} 

{{{highlight(x = -6) }}} 

or

{{{x = (-15 - 3)/2 }}} 

{{{x = -18/2 }}} 

{{{highlight(x = -9) }}}