Question

Solve the following equation:
$4^{\log x+1}-6^{\log x}-2\cdot 3^{\log x^2+2}=0$

Answer 1

$4^{logx+1}-6^{logx}-{2.3}^{{logx}^2+2}=0$

Let $2^{logx}=a,3^{logx}=b$

${4a}^2-ab-{18b}^2=0\Rightarrow 4a^2+8ab-9ab-{18b}^2=0\Rightarrow 4a(a+2b)-9b(a+2b)=0\Rightarrow 4a=9b$

$(\because a+2b$ never be $0)$

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

$\Rightarrow x=\frac{1}{100}$