Question 911885
{{{ log(7,(x+4)) +log(7,(x-2)) = 1 }}}

{{{ log(7,(x+4)(x-2)) = 1 }}} ...........{{{log(7,7) = 1}}}


{{{ log(7,(x+4)(x-2)) = log(7,7)}}} same log =>

{{{ (x+4)(x-2) = 7}}}

{{{ x^2-2x+4x-8 = 7}}}

{{{ x^2+2x-8 -7= 0}}}

{{{ x^2+2x-15= 0 }}} .......{{{2x}}} as {{{5x-3x}}}

{{{x^2+5x-3x-15 = 0}}} ...group

{{{(x^2+5x)-(3x+15) = 0}}} ...factor

{{{x(x+5)-3(x+5) = 0}}}

{{{(x-3)(x+5) = 0}}}

solutions:

if {{{(x-3)= 0}}} => {{{highlight(x=3)}}} ...we need only this one since log

if {{{(x+5)= 0}}} => {{{x=-5}}}


{{{ graph( 600, 600, -10, 10, -10, 10, log(7,(x+4))+log(7,(x-2)), 1) }}}