Giải:
a) \(\left(x+2\right)^5=\left(x+2\right)^2\)
Vì \(x+2=x+2\)
Mà \(5e2\)
\(\Leftrightarrow\left(x+2\right)=\left\{0;1\right\}\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+2=0\\x+2=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-2\\x=-1\end{matrix}\right.\)
Vậy \(x=-2\) hoặc \(x=-1\)
b) \(2^{3x+4}=4^{x+8}\)
\(\Leftrightarrow2^{3x+4}=\left(2^2\right)^{x+8}\)
\(\Leftrightarrow2^{3x+4}=2^{2x+16}\)
Vì \(2=2\)
Nên \(3x+4=2x+16\)
\(\Leftrightarrow3x-2x=16-4\)
\(\Leftrightarrow x=12\)
Vậy \(x=12\).
c) \(3^{x+2}=9^{x-1}\)
\(\Leftrightarrow3^{x+2}=\left(3^2\right)^{x-1}\)
\(\Leftrightarrow3^{x+2}=3^{2x-2}\)
Vì \(3=3\)
Nên \(x+2=2x-2\)
\(\Leftrightarrow2x-2=2+2\)
\(\Leftrightarrow x=4\)
Vậy \(x=4\).
d) \(9^{x-2}=27^{x-4}\)
\(\Leftrightarrow\left(3^2\right)^{x-2}=\left(3^3\right)^{x-4}\)
\(\Leftrightarrow3^{2x-4}=3^{3x-12}\)
Vì \(3=3\)
Nên \(2x-4=3x-12\)
\(\Leftrightarrow x=8\)
Vậy \(x=8\).
Chúc bạn học tốt!!!
