Question

Solve:${\log }_{10}\left(\frac{5x-x^2}{4}\right)=0$

Answer 1

${\log }_{10}\left(\frac{5x-x^2}{4}\right)=0$

$\Rightarrow \frac{5x-x^2}{4}={10}^0=1$

$\Rightarrow 5x-x^2=4$

$\Rightarrow -x^2+5x-4=0$

$\Rightarrow x^2-5x+4=0$

$\Rightarrow x^2-4x-x+4=0$

$\Rightarrow x(x-4)-1(x-4)=0$

$\Rightarrow (x-4)(x-1)=0$

$\therefore x=1,4$

But $x\ne 4$ because for $x=4$ logarithm is not defined

$\therefore x=1$