ra đi ra lại không chán hả

\(2^x+2^{x+4}=544\Leftrightarrow2^x\left(1+2^4\right)=544\)

\(\Leftrightarrow2^x=\frac{544}{17}=32=2^5\Rightarrow x=5\)

~ Học tốt ~

tổng trên có số số hạng là: \(\frac{\left(x-2\right)}{2}+1=\frac{x}{2}-1+1=\frac{x}{2}\)

tổng của dãy là: \(\frac{\left(x+2\right)x}{2}=544\Leftrightarrow\frac{x^2}{2}+x-544=0\Leftrightarrow x^2+2x-1088=0\Leftrightarrow x^2-32x+34x-1008=0\Leftrightarrow\left(x-32\right)\left(x+34\right)=0\)

=> x=32(t/m)  hoặc x=-34(loại)

=> x=32

Ta có : 2^x + 2^{x + 4} = 544

=> 2^x(1 + 2⁴) = 544

=> 2^x.17 = 544

=> 2^x = 32

=> 2^x = 2⁵

=> x = 5

Vậy x = 5

\(a,\Leftrightarrow2^x\left(1+2^4\right)=544\\ \Leftrightarrow2^x=\dfrac{544}{17}=32=2^5\\ \Leftrightarrow x=5\\ b,\Leftrightarrow\left(\dfrac{2}{5}-3x\right)^2=\dfrac{9}{25}\Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{5}-3x=\dfrac{3}{5}\\3x-\dfrac{2}{5}=\dfrac{3}{5}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}3x=-\dfrac{1}{5}\\3x=1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{1}{15}\\x=\dfrac{1}{3}\end{matrix}\right.\)

Sửa lại đề

\(2^x+2^x+4=516\)

\(\Rightarrow2^x+2^x=512\)

\(\Rightarrow2^x+2^x=2^8+2^8\)

\(\Rightarrow x=8\)

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\(2^x+2^{x+4}=544\)

\(2^x\left(1+2^4\right)=544\)

\(2^x.17=544\)

\(2^x=32\)

\(2^x=2^5\)

\(\Rightarrow x=5\)

\(\Leftrightarrow2^x\left(1+2^4\right)=544\\ \Leftrightarrow2^x\cdot17=544\\ \Leftrightarrow2^x=32=2^5\Leftrightarrow x=5\)

\(2^x+2^{x+4}=544\\\Rightarrow2^x\cdot1+2^x\cdot2^4=544\\\Rightarrow2^x\cdot(1+2^4)=544\\\Rightarrow2^x\cdot(1+16)=544\\\Rightarrow2^x\cdot17=544\\\Rightarrow2^x=544:17\\\Rightarrow2^x=32\\\Rightarrow2^x=2^5\\\Rightarrow x=5\)

\(2^x+2^{x+4}=544\)

=>\(2^x+2^x\cdot2^4=544\)

=>\(2^x\left(1+2^4\right)=544\)

=>\(2^x\cdot17=544\)

=>\(2^x=\dfrac{544}{17}=32\)

=>\(2^x=2^5\)

=>x=5