Question

Solve:$7^{{\log }_{7}x}+2x+9=0$

Answer 1

$7^{{\log }_{7}x}+2x+9=0$

$\Rightarrow x+2x+9=0$ since $a^{{\log }_{a}x}=x$

$\Rightarrow 3x+9=0$

$\Rightarrow 3x=-9$

$\Rightarrow x=\frac{-9}{3}=-3$

$\therefore x=-3$

But $\log$ is not defined for negative value

$\therefore$ there is no slotion

Hence $x\in \varphi$