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a: =>x=(-2/3)^5:(-2/3)^2=(-2/3)^3=-8/27
b: =>x*(-1/3)^3=(-1/3)^4
=>x=-1/3
d: =>3x-2=-3
=>3x=-1
=>x=-1/3
`@` `\text {Ans}`
`\downarrow`
`a)`
`2^2 * 16 \ge 2^x \ge 4^2`
`=> 2^2 * 2^4 \ge 2^x \ge 2^4`
`=> 2^6 \ge 2^x \ge 2^4`
`=> x \in {4; 5; 6}`
`b)`
`9*27 \le 3^x \le 243`
`=> 3^2 * 3^3 \le 3^x \le 3^5`
`=> 3^5 \le 3^x \le 3^5`
`=> x = 5`
`c)`
`2 * (x - 1/2)^2 - 1/8 = 0`
`=> 2* (x - 1/2)^2 = 1/8`
`=> (x - 1/2)^2 = 1/8 \div 2`
`=> (x-1/2)^2 = 1/16`
`=> (x - 1/2)^2 = (+- 1/4)^2`
`=>`\(\left[{}\begin{matrix}x-\dfrac{1}{2}=\dfrac{1}{4}\\x-\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=\dfrac{1}{4}+\dfrac{1}{2}\\x=\dfrac{1}{2}-\dfrac{1}{4}\end{matrix}\right.\)
`=>`\(\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{1}{4}\end{matrix}\right.\)
Vậy, `x \in {1/4; 3/4}.`
\(a,\Rightarrow\left(x-\dfrac{1}{2}\right)^3=\dfrac{1}{27}=\left(\dfrac{1}{3}\right)^3\\ \Rightarrow x-\dfrac{1}{2}=\dfrac{1}{3}\Rightarrow x=\dfrac{5}{6}\\ b,\Rightarrow\left(\dfrac{3}{2}\right)^{2x-1}:\left(\dfrac{3}{2}\right)^9=\left(\dfrac{3}{2}\right)^4\\ \Rightarrow2x-1-9=4\\ \Rightarrow2x=14\Rightarrow x=7\\ c,\Rightarrow2^{x-1}+2^{x+2}=9\cdot2^5\\ \Rightarrow2^{x-1}\left(1+2^3\right)=9\cdot2^5\\ \Rightarrow2^{x-1}\cdot9=9\cdot2^5\\ \Rightarrow2^{x-1}=2^5\Rightarrow x-1=5\Rightarrow x=6\\ d,\Rightarrow\left(2x+1\right)^2=12+69=81\\ \Rightarrow\left[{}\begin{matrix}2x+1=9\\2x+1=-9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=4\\x=-5\end{matrix}\right.\)
h) \(5^x+5^{x+2}=650\)
\(\Leftrightarrow5^x+5^x.5^2=650\)
\(\Leftrightarrow5^x\left(1+25\right)=650\)
\(\Leftrightarrow5^x.26=650\)
\(\Leftrightarrow5^x=25\)
\(\Leftrightarrow x=2\)
haizzz,đăng ít thôi,chứ nhìn hoa mắt quá =.=
bây định làm j ở chỗ này vậy??? có j ib ns vs nhao chớ sao ns ở đây
\(1,\Leftrightarrow\left[{}\begin{matrix}2x-1=5\\1-2x=5\end{matrix}\right.\Leftrightarrow D\\ 2,\Leftrightarrow\left(-3\right)^x=-27\cdot81=-2187=\left(-3\right)^7\\ \Leftrightarrow x=7\left(A\right)\)
\(a,\Rightarrow2^3< 2^x\le2^4\Rightarrow x=4\\ b,\Rightarrow3^3< 3^{12}:3^x< 3^5\\ \Rightarrow3^3< 3^{12-x}< 3^5\\ \Rightarrow12-x=4\Rightarrow x=8\)
Câu a)
\(2\left(x-1\right)-3\left(2x+2\right)-4\left(2x+3\right)=16\)
\(\Leftrightarrow2x-2-6x-6-8x-12=16\)
\(\Leftrightarrow-12x-20=16\)
\(\Leftrightarrow-12x=16+20\)
\(\Leftrightarrow-12x=36\)
\(\Leftrightarrow x=-3\)
Vậy \(x=-3\)
Câu c)
\(\dfrac{2x-y}{5}=\dfrac{3x-2z}{15}\) \(\Rightarrow\dfrac{3\left(2x-y\right)}{3\times5}=\dfrac{3x-2z}{15}\) \(\Rightarrow\dfrac{6x-3y}{15}=\dfrac{3x-2z}{15}\)
\(\Rightarrow6x-3y=3x-2z\)
\(\Rightarrow6x-3x+2z=3y\)
\(\Rightarrow3x+2z=3y\)
\(\Rightarrow\left(2x+2z\right)+x=3y\)
\(\Rightarrow2\left(x+z\right)+x=3y\)
\(\Rightarrow2\times2y+x=3y\)
\(\Rightarrow4y+x=3y\)
\(\Rightarrow x=3y-4y\)
\(\Rightarrow x=-y\)
a,\(x:\left(\dfrac{-3}{5}\right)^2=\dfrac{-3}{5}\)
\(\Leftrightarrow x=\dfrac{-3}{5}.\dfrac{9}{25}\Leftrightarrow x=\dfrac{-27}{125}\)
b,\(\left(\dfrac{-1}{3}\right)^3.x=\dfrac{1}{81}\)
\(\Leftrightarrow x=.\dfrac{1}{81}:\left(\dfrac{-1}{27}\right)\Leftrightarrow x=\dfrac{-1}{3}\)
c,(2x2)=16\(\Leftrightarrow\)x2=8\(\Leftrightarrow\)x=\(,\sqrt{8}\)
Giải:
a. \(x:\left(\dfrac{-3}{5}\right)^2=\dfrac{-3}{5}\)
\(\Rightarrow x=\left(\dfrac{-3}{5}\right)^2.\dfrac{-3}{5}\)
\(\Rightarrow x=\left(\dfrac{-3}{5}\right)^3\)
\(\Rightarrow x=\dfrac{-27}{125}\)
Vậy.................
b.\(\left(\dfrac{-1}{3}\right)^3.x=\dfrac{1}{81}\)
\(\Rightarrow x=\dfrac{1}{81}:\left(\dfrac{-1}{3}\right)^3\)
\(\Rightarrow x=\dfrac{1}{81}:\dfrac{-1}{27}\)
\(\Rightarrow x=\dfrac{1}{81}.\dfrac{-27}{1}\)
\(\Rightarrow x=\dfrac{1}{3}.\dfrac{-1}{1}\)
\(\Rightarrow x=\dfrac{-1}{3}\)
vậy................
c.\(\left(2x^2\right)=16\)
\(\Rightarrow2x=\sqrt{16}=4\)
\(\Rightarrow x=4:2\)
\(\Rightarrow x=2\)
vậy....................
Lời giải:
a.
$(\frac{-1}{3})^3.x=\frac{1}{81}=(\frac{-1}{3})^4$
$\Rightarrow x=(\frac{-1}{3})^4: (\frac{-1}{3})^3=\frac{-1}{3}$
b.
$2^2.16> 2^x> 4^2$
$\Rightarrow 2^2.2^4> 2^x> (2^2)^2$
$\Rightarrow 2^6> 2^x> 2^4$
$\Rightarrow 6> x> 4$
$\Rightarrow x=5$ (với điều kiện $x$ là số tự nhiên nhé)
c.
$9.27< 3^x< 243$
$3.3^3< 3^x< 3^5$
$\Rightarrow 3^4< 3^x< 3^5$
$\Rightarrow 4< x< 5$
Với $x$ là stn thì không có số nào thỏa mãn.