Toán Lớp 6: 4.5 mũ x +1 =500
(x mũ 54) mũ 2=x
2 mũ x + mũ 3 + 2 mũ x=144
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Toán Lớp 6: 4.5 mũ x +1 =500
(x mũ 54) mũ 2=x
2 mũ x + mũ 3 + 2 mũ x=144
Comments ( 2 )
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}$
=> 3^x : 3 = 1/243
=>3^x = 3/243 = 1/81
=> x = -4 ( vì 3^-4 = 1/(3^4) = 1/81)
2^x + 2^(x + 3) = 144
=> 2^x + 2^x.2^3 = 144
=> 2^x ( 1 + 2^3) = 144