`a) (5x - 1)^6 = 729`
`=> (5x - 1)^6 = 3^6`
=> \(\left[ \begin{array}{l}5x - 1 = 3\\5x - 1 = -3\end{array} \right.\)
=> \(\left[ \begin{array}{l}5x = 4\\5x = -2\end{array} \right.\)
=> \(\left[ \begin{array}{l}x /frac{4}{5}\\x =/frac{-2}{5}\end{array} \right.\)
`b) (2n + 1)^3 = -0,001`
`=> (2n + 1)^3 = -0,1^3`
`=> 2n + 1 = -0,1`
`=> 2x = -1,1`
`=> x = -0,55`
`c) (2x - 3)^4 = (2n - 3)^6`
`=> (2n - 3)^6 - (2x - 3)^4 = 0`
`=> (2x - 3)^4 . ((2n - 3)^2 - 1) = 0`
Xét `(2x - 3)^4 = 0 => 2x - 3 = 0 => 2x = 3 => x = 3/2`
Xét `(2n - 3)^2 - 1 = 0 => (2n - 3)^2 = 1`
=> \(\left[ \begin{array}{l}2n - 3=1\\2n - 3=-1\end{array} \right.\)
=> \(\left[ \begin{array}{l}2n =4\\2n =-2\end{array} \right.\)
=> \(\left[ \begin{array}{l}n=2\\n=-1\end{array} \right.\)
d) `(2x+1)^5 = (2x+1)^2019`
`=> (2x+1)^2019 - (2x+1)^5 = 0`
`=> (2x+1)^5 . ((2x+1)^2014 - 1) = 0`
Xét `(2x+1)^5 = 0 => 2x + 1 = 0 => 2x = -1 => x = -1/2`
Xét `(2x+1)^2014 - 1 = 0 => (2x+1)^2014 = 1`
=>\(\left[ \begin{array}{l}2x+1=1\\2x+1=-1\end{array} \right.\)
=> \(\left[ \begin{array}{l}2n =0\\2n =-2\end{array} \right.\)
=> \(\left[ \begin{array}{l}n=0\\n-1\end{array} \right.\)
------------------------------------------------------------------
`3^x + 3^(x+3) = 756`
`=> 3^x + 3^x . 3^3 = 756`
`=> 3^x (1+27) = 756`
`=> 3^x . 28 = 756`
`=> 3^x = 27`
`=> 3^x = 3^3`
`=> x = 3`
`5^(x+1) + 6.5^(x+1) = 875`
`=> 5^(x+1) ( 1+6) = 875`
`=> 5^(x+1) . 7 = 875`
`=> 5^(x+1) = 125`
`=> 5^(x+1) = 5^3`
`=> x + 1 = 3`
`=> x = 2`
`(x-7)^(x+1) - (x-7)^(x+11) = 0`
=> `(x-7)^(x+1) . (1 - (x-7)^(x+10)) = 0`
Xét `(x-7)^(x+1) = 0 => x-7 = 0 => x = 7`
Xét `1 - (x-7)^(x+10) = 0 => (x-7)^(x+10) = 1`
=> `x` là số chẵn `=> x+10` là số chẵn
=>\(\left[ \begin{array}{l}x-7=1\\x-7=-1\end{array} \right.\)
=> \(\left[ \begin{array}{l}x=8\\x = 6\end{array} \right.\)
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