Question 331639
{{{ log( x ) + log ( (x-15) ) = 2 }}}

{{{ log( x )*(x-15) = 2 }}}

{{{log((x^2-15x)) = 2 }}}

{{{ 10^(log(x^2-15x)) = 10^2 }}}

{{{ x^2-15x = 100 }}}
{{{ x^2 - 15x - 100 =0 }}}  factor

(x-20)*(x+5)=0

either X=20 or X=-5
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check X=20, by substituting in original equation
Log 20 + log(20-15) =2
log 20 +log 5=2
{{{log 20*5=log 100=log 10^2 =2}}}
2log10=2
2=2  verifies X=20 as a solution
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check X=-5
log(-5)+log(-5-15)=2  STOP!!!! log functions are define for values greater than 0, 
so X=-5 is not a solution