Question

Solve the following equation:
$3^{2x+1}+10.3^x+3=0$

Answer 1

$3^{2x+1}+10\cdot 3^x+3=0$

$\Rightarrow 3\cdot 3^{2x}+10\cdot 3^x+3=0$

$\Rightarrow 3(3^x{)}^2+10(3^x)+3=0$

is the quadratic equation in $3^x$

$\Rightarrow 3(3^x{)}^2+(9+1\left)\right(3^x)+3=0$

$\Rightarrow \left(3\right(3^x)+1)(3^x+3)=0$

$\Rightarrow (3^x=\frac{-1}{3})(3^x=-3)$

$\Rightarrow$ No. of values of x as log in undefined for a negative input,

$\Rightarrow x\log 3=-1\log (-3)=\infty$

$\Rightarrow x\log 3=\log (-3)=\infty$