\(a.\left(x^{54}\right)^2=x\)
\(\Rightarrow x^{108}=x\)
\(\Leftrightarrow x^{108}-x=0\)
\(\Leftrightarrow x.\left(x^{107}-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^{107}=0\Leftrightarrow x^{107}=1\Leftrightarrow x=1\end{cases}}\)
Vậy \(\orbr{\begin{cases}x=0\\x=1\end{cases}}\)
a) ( x54 )2 = x
=> ( x54 )2 - x = 0
=> x108 - x = 0
=> x(x107 - 1 ) = 0
=> x107 - 1 = 0
=> x107 = 1
=> x107 = 1107
=> x = 1
b) 2x+3+ 2x = 144
=> 2x . 23 + 2x = 144
=> 2x . ( 23 + 1 ) = 144
=> 2x . 9 = 144
=> 2x = 16
=> x = 4
\(2^{x+3}+2^x=144\)
\(\Leftrightarrow2^x.2^3+2^x=144\)
\(\Leftrightarrow2^x.\left(8+1\right)=144\)
\(\Leftrightarrow2^x.9=144\)
\(\Leftrightarrow2^x=144:9=16\)
\(\Leftrightarrow2^x=2^4\Leftrightarrow x=4\)