Question

3*8^x+4*12^x-18^x-2*27^x=0

Answer 1

$displaystyle 3*8^x+4*12^x-18^x-2*27^x=0\\3*2^{3x}+4*2^{2x}*3^x-2^x*3^{2x}-2*3^{3x}=0| :3^{3x}\\3*(frac{2}{3})^{3x}+4* (frac{2}{3})^{2x}- (frac{2}{3})^x-2=0\\ (frac{2}{3})^x=t\\3t^3+4t^2-t-2=0\\(t+1)^2(3t-2)=0\\t=-1; t= frac{2}{3}\\ (frac{2}{3})^x neq -1\\(frac{2}{3})^x= frac{2}{3}\\x=1$