Question

Solve:
${\log }_{5-x}(x^2-6x+65)=2$

Answer 1

$lo{g}_{5-x}(x^2-2x+65)=2$

$x^2-2x+65=(5-x{)}^2$

$x^2-2x+65=5^2+x^2-\mathrm{2.5.}x$

$x^2-2x+65=x^2-10x+25$

$-2x+10x+65-25=0$

$8x+40=0$

$x+5=0$

$x=-5$.

$\therefore x=-5$

Let us check $x=-5$ is

correct or not.

$lo{g}_{5-(-5)}\left(\right(-5{)}^2-2(-5)+65)$

$lo{g}_{10}(25+10+65)$

$log100$

$log{10}^2$

$=2$