Question

Solve the following equation:
${\log }_3({4.3}^x-1)=2x+1$

Answer 1

${log}_3({4.3}^x-1)=2x+1\Rightarrow {4.3}^x-1=3^{(2x+1)}\Rightarrow {4.3}^x-1=3^{(2x+1)}\Rightarrow 4\left(3^x\right)-1={{(3}^x)}^2.3\Rightarrow 3(3^x{)}^2-4(3^x)+1=0$

Therefore, $3^x=\frac{1}{3}$ or $3^x=1$

Therefore, $x=-1$ or $0.$