Question

Solve:
${\log }_{10}x+{\log }_{10}(x-15)=2,x>0$

Answer 1

Given,

${\log }_{10}x+{\log }_{10}(x-15)=2$

or, ${\log }_{10}x(x-15)=2$

or, $x(x-15)={10}^2$

or, $x^2-15x-100=0$

or, $(x-20)(x+5)=0$

or, $x=20$ [ Since $x>0$].