$\\$
`a,`
`3^{(x-1) (x-2)}=1`
`-> 3^{(x-1) (x-2)}=3^0`
`-> (x-1) (x-2)=0`
`->` \(\left[ \begin{array}{l}x-1=0\\x-2=0\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=0+1\\x=0+2\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=1\\x=2\end{array} \right.\)
Vậy `x=1` hoặc `x=2`
$\\$
`b,`
`5 . 2007^{(x-2) (x-3)} -5=0`
`-> 5 . 2007^{(x-2) (x-3)}=0+5`
`->5 . 2007^{(x-2) (x-3)}=5`
`-> 2007^{(x-2) (x-3)}=5:5`
`-> 2007^{(x-2) (x-3)}=1`
`-> 2007^{(x-2) (x-3)=2007^0`
`-> (x-2) (x-3)=0`
`->` \(\left[ \begin{array}{l}x-2=0\\x-3=0\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=0+2\\x=0+3\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=2\\x=3\end{array} \right.\)
Vậy `x=2` hoặc `x=3`
$\\$
`c,`
`2 - 2 . 5^{x^2-4}=0`
`-> 2 . 5^{x^2 - 4}=2-0`
`-> 2 . 5^{x^2-4}=2`
`-> 5^{x^2-4}=2:2`
`-> 5^{x^2-4}=1`
`->5^{x^2-4}=5^0`
`->x^2-4=0`
`->x^2=0+4`
`->x^2=4`
`->` \(\left[ \begin{array}{l}x^2=2^2\\x^2=(-2)^2\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=2\\x=-2\end{array} \right.\)
Vậy `x=2` hoặc `x=-2`
$\\$
`d,`
`25^{x^2 - 1} -1=0`
`->25^{x^2-1}=0+1`
`-> 25^{x^2-1}=1`
`-> 25^{x^2-1}=25^0`
`-> x^2-1=0`
`->x^2=0+1`
`->x^2=1`
`->` \(\left[ \begin{array}{l}x^2=1^2\\x^2=(-1)^2\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=1\\x=-1\end{array} \right.\)
Vậy `x=1` hoặc `x=-1`
$\\$
`e,`
`3^{-2} . 2000^{(x-3) (x-5)} =1/9`
`-> 1/9 . 2000^{(x-3) (x-5)}=1/9`
`-> 2000^{(x-3) (x-5)}=1/9 : 1/9`
`-> 2000^{(x-3) (x-5)}=1`
`-> 2000^{(x-3) (x-5)}=2000^0`
`-> (x-3) (x-5)=0`
`->` \(\left[ \begin{array}{l}x-3=0\\x-5=0\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=0+3\\x=0+5\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=3\\x=5\end{array} \right.\)
Vậy `x=3` hoặc `x=5`
`f,`
`2^{-1} . 2005^{9-x^2} =1/2`
`-> 1/2 . 2005^{9-x^2}=1/2`
`-> 2005^{9-x^2}=1/2 : 1/2`
`-> 2005^{9-x^2}=1`
`-> 2005^{9-x^2}=2005^0`
`->9-x^2=0`
`->x^2=9-0`
`->x^2=9`
`->` \(\left[ \begin{array}{l}x^2=3^2\\x^2=(-3)^2\end{array} \right.\) `->` \(\left[ \begin{array}{l}x=3\\x=-3\end{array} \right.\)
Vậy `x=3` hoặc `x=-3`
