Question 914744

{{{log(5, ((x + 5)) )+ log( 5, ((x- 5))) = 2 }}}


{{{log(5, ((x + 5)(x -5))) = 2 }}}


{{{log(5, ( x^2 - 25)) = 2 }}}...............a single logarithm


{{{log( (x^2 -25))/log(5) = 2 }}}


{{{log( ( x^2 - 25))= 2 log(5) }}}


{{{log( (x^2 - 25))=  log((5^2)) }}}


{{{log(  (x^2 - 25))=  log(25) }}} .....if log same, than


{{{x^2 - 25=  25 }}} ....solve for {{{x}}}


{{{x^2 =  25 +25}}}


{{{x^2 = 2*25}}}


{{{x = sqrt(2*25)}}}


solution


{{{x = 5sqrt(2)}}}