Đáp án:
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`a,`
`(2x-1)^4=81`
`↔` \(\left[ \begin{array}{l}(2x-1)^4=3^4\\(2x-1)^4=(-3)^4\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x-1=3\\2x-1=-3\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x=3+1\\2x=-3+1\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}2x=4\\2x=-2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=4÷2\\x=-2÷2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=2\\x=-1\end{array} \right.\)
Vậy `x=2` hoặc `x=-1`
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`b,`
`(x-1)^5 = -32`
`↔ (x-1)^5 = (-2)^5`
`↔ x-1=-2`
`↔x=-2+1`
`↔x=-1`
Vậy `x=-1`
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`c,`
`(3x+2)^6 = (3x+2)^4`
`↔ (3x+2)^6 - (3x+2)^4=0`
`↔ (3x+2)^4 × (3x+2)^2 - (3x+2)^4=0`
`↔ (3x+2)^4 × [(3x+2)^2-1]=0`
`↔` \(\left[ \begin{array}{l}(3x+2)^4=0\\(3x+2)^2-1=0\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}3x+2=0\\(3x+2)^2=1\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}3x=-2\\(3x+2)^2=1^2\\(3x+2)^2=(-1)^2\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=\dfrac{-2}{3}\\3x+2=1\\3x+2=-1\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=\dfrac{-2}{3}\\3x=-1\\3x=-3\end{array} \right.\)
`↔` \(\left[ \begin{array}{l}x=\dfrac{-2}{3}\\x=\dfrac{-1}{3}\\x=-1\end{array} \right.\)
Vậy `x=(-2)/3,x=(-1)/3,x=-1`
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`d,`
`5^x + 5^{x+2} = 650`
`↔ 5^x +5^x × 5^2 = 650`
`↔ 5^x × (1 + 5^2) = 650`
`↔ 5^x × (1 + 25) = 650`
`↔ 5^x × 26 = 650`
`↔ 5^x = 650 ÷ 26`
`↔ 5^x=25`
`↔ 5^x=5^2`
`↔x=2`
Vậy `x=2`
