Question 1001259

{{{ ln(x+4)=ln(x-8)-ln(x+1) }}}

{{{ ln(x+4)=ln((x-8)/(x+1)) }}}........if log same, we have

{{{ (x+4)=(x-8)/(x+1) }}}.......solve for {{{x}}}

{{{ (x+4)(x+1)=(x-8) }}}

{{{ x^2+x+4x+4=x-8 }}}

{{{ x^2+cross(x)+4x+4-cross(x)+8=0 }}}

{{{ x^2+4x+12=0 }}}....use quadratic formula

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

{{{x = (-4 +- sqrt( 4^2-4*1*12 ))/(2*1) }}} 

{{{x = (-4 +- sqrt( 16-48 ))/2 }}} 

{{{x = (-4 +- sqrt( -32 ))/2 }}} 

{{{x = (-4 +- sqrt( -16*2 ))/2 }}}

{{{x = (-4 +- 4i*sqrt( 2 ))/2 }}}

{{{x = (-2 +- 2i*sqrt( 2 )) }}}

solutions:
{{{x = (-2 + 2i*sqrt( 2 )) }}}
or
{{{x = (-2 - 2i*sqrt( 2 )) }}}




{{{ log(6 ,(2-x)) + log(6, (11-x)) = 2 }}}....change the base

{{{ log((2-x))/log((6))  + log( (11-x))/log((6)) = 2 }}}

{{{ (log((2-x))  + log( (11-x)))/log((6)) = 2 }}}

{{{ (log((2-x))  + log( (11-x))) = 2log((6)) }}}

{{{ log((2-x)(11-x)) = log((6^2)) }}}

{{{ log((2-x)(11-x)) = log((36)) }}}.....if log same, we have

{{{ (2-x)(11-x) = 36 }}}....solve for {{{x}}}

{{{ 22-2x-11x+x^2 = 36 }}}

{{{ x^2-13x +22-36=0 }}}

{{{ x^2-13x -14=0 }}}

{{{ x^2+x-14x -14=0 }}}

{{{( x^2+x)-(14x +14)=0 }}}

{{{x( x+1)-14(x +1)=0 }}}

{{{(x-14)(x +1)=0 }}}

solutions:

if {{{(x-14)=0 }}}=>{{{x=14}}}-> disregard it it will make log of negative number which is undefined

if {{{(x +1)=0 }}}=>{{{highlight(x=-1)}}}