4.5 mũ x +1 =500 (x mũ 54) mũ 2=x 2 mũ x + mũ 3 + 2 mũ x=144

Đáp án:

$\begin{array}{l}
a){4.5^{x + 1}} = 500\\
 \Leftrightarrow {5^{x + 1}} = 500:4\\
 \Leftrightarrow {5^{x + 1}} = 125\\
 \Leftrightarrow {5^{x + 1}} = {5^3}\\
 \Leftrightarrow x + 1 = 3\\
 \Leftrightarrow x = 2\\
Vậy\,x = 2\\
b){\left( {{x^{54}}} \right)^2} = x\\
 \Leftrightarrow {x^{54.2}} - x = 0\\
 \Leftrightarrow {x^{108}} - x = 0\\
 \Leftrightarrow x.\left( {{x^{107}} - 1} \right) = 0\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
{x^{107}} - 1 = 0
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
{x^{107}} = 1
\end{array} \right.\\
 \Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = 1
\end{array} \right.\\
Vậy\,x = 0;x = 1\\
c){2^{x + 3}} + {2^x} = 144\\
 \Leftrightarrow {2^x}{.2^3} + {2^x} = 144\\
 \Leftrightarrow {2^x}.\left( {{2^3} + 1} \right) = 144\\
 \Leftrightarrow {2^x} = 144:9 = 16\\
 \Leftrightarrow {2^x} = {2^4}\\
 \Leftrightarrow x = 4\\
Vậy\,x = 4
\end{array}$