a/ \(\dfrac{\left(-3\right)^x}{81}=-27\)
\(\Leftrightarrow\left(-3\right)^x=\left(-27\right).81\)
\(\Leftrightarrow\left(-3\right)^x=-2187\)
\(\Leftrightarrow\left(-3\right)^x=\left(-3\right)^7\)
\(\Leftrightarrow x=7\)
Vậy ...
b/ \(2^{x-1}=16\)
\(\Leftrightarrow2^{x-1}=2^4\)
\(\Leftrightarrow x-1=4\)
\(\Leftrightarrow x=5\)
Vậy ....
c/ \(\left(x-1\right)^2=25\)
\(\Leftrightarrow\left(x-1\right)^2=5^2=\left(-5\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=5\\x-1=-5\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\)
Vậy ....
d/ \(0,2-\left|4,2-2x\right|=0\)
\(\Leftrightarrow\left|4,2-2x\right|=0,2\)
\(\Leftrightarrow\left[{}\begin{matrix}4,2-2x=0,2\\4,2-2x=-0,2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=4\\2x=4,4\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=2,2\end{matrix}\right.\)
Vậy ............
e, \(1\dfrac{2}{3}:\dfrac{x}{4}=6:0,3\)
\(\Leftrightarrow\dfrac{5}{3}.\dfrac{4}{x}=20\)
\(\Leftrightarrow3x=1\)
\(\Leftrightarrow x=\dfrac{1}{3}\)
Vậy ..
a) \(\dfrac{\left(-3\right)^x}{81}=-27\)
⇔ \(\dfrac{\left(-3\right)^x}{81}=\dfrac{-2187}{81}\)
⇔ (-3)x = -2187
⇔ (-3)x = (-3)7
⇔ x = 7
b) 2x-1 = 16
⇔ 2x-1 = 24
⇔ x - 1 = 4
⇔ x = 4 + 1
⇔ x = 5
c) (x - 1)2 = 25
⇔ \(\left[{}\begin{matrix}\left(x-1\right)^2=5^2\\\left(x-1\right)^2=\left(-5\right)^2\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}x-1=5\\x-1=-5\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}x=5+1\\x=-5+1\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}x=6\\x=-4\end{matrix}\right.\)
d) 0,2 - |4,2 - 2x| = 0
⇔ |4,2 - 2x| = 0,2
⇔ \(\left[{}\begin{matrix}4,2-2x=0,2\\4,2-2x=-0,2\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}2x=4,2-0,2\\2x=4,2-\left(-0,2\right)\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}2x=4\\2x=4,4\end{matrix}\right.\)
⇔ \(\left[{}\begin{matrix}x=2\\x=2,2\end{matrix}\right.\)
e) \(1\dfrac{2}{3}:\dfrac{x}{4}=6:0,3\)
⇔ \(\dfrac{5}{3}.\dfrac{4}{x}=20\)
⇔ \(\dfrac{20}{3x}=20\)
⇔ 3x = 1
⇔ x = \(\dfrac{1}{3}\)