Question

Solve the following equations.
$(3^{x^2-7.2x+3.9}-9\sqrt{3})\log (7-x)=0$

Answer 1

$(3^{x^2-7.22x+3.9}-9\sqrt{3})\left(log\right(7-x\left)\right)=0$

$\Rightarrow 3^{x^2-7.2x+3.9-9\sqrt{3}}=0$ (assuming $log(7-x)\ne 0)$

$\Rightarrow 3^{x^2-7.2x+3.9}=3^{2+\frac{1}{2}}$

$\Rightarrow x^2-7.2x+3.9=2.5$

$\Rightarrow x^2-7.2x+1.4=0$

$\Rightarrow x=\frac{1\pm \sqrt{(7.2{)}^2-4\times 1\times 1.4}}{2\times 1}$

$\Rightarrow x=\frac{1}{2}\pm \sqrt{11.56}$

$=\frac{1}{2}\pm 3.4$

$=3.9-2.9$

if $log(7-x)=0$

$\Rightarrow 7-x=1$

$\Rightarrow x=6$

$x=6,3.9,-2.9$