a:
ĐKXĐ: \(x\in R\)
\(log_2\left(x^2-x+2\right)=1\)
=>\(x^2-x+2=2^1=2\)
=>\(x^2-x=0\)
=>x(x-1)=0
=>\(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
b: ĐKXĐ: \(x^2+2x>0\)
=>\(\left[{}\begin{matrix}x>0\\x< -2\end{matrix}\right.\)
\(log_3\left(x^2+2x\right)=1\)
=>\(x^2+2x=3^1=3\)
=>\(x^2+2x-3=0\)
=>(x+3)(x-1)=0
=>\(\left[{}\begin{matrix}x=-3\left(nhận\right)\\x=1\left(nhận\right)\end{matrix}\right.\)
c: \(3^{x^2-4}=\left(\dfrac{1}{9}\right)^{3x-1}\)
=>\(3^{x^2-4}=3^{-6x+2}\)
=>\(x^2-4=-6x+2\)
=>\(x^2+6x-6=0\)
=>\(\left(x+3\right)^2-15=0\)
=>\(x=\pm\sqrt{15}-3\)
d: \(2^{x^2+2x}=8^{2-x}\)
=>\(2^{x^2+2x}=2^{6-3x}\)
=>\(x^2+2x=6-3x\)
=>\(x^2+5x-6=0\)
=>(x+6)(x-1)=0
=>\(\left[{}\begin{matrix}x=-6\\x=1\end{matrix}\right.\)
e: \(27^{2x-3}=\left(\dfrac{1}{3}\right)^{x^2+2}\)
=>\(3^{-x^2-2}=3^{6x-9}\)
=>\(-x^2-2=6x-9\)
=>\(x^2+2+6x-9=0\)
=>\(x^2+6x-7=0\)
=>(x+7)(x-1)=0
=>\(\left[{}\begin{matrix}x=-7\\x=1\end{matrix}\right.\)
