a, 7\(x\) - \(x\) = 521 : 519 + 3.22.7
6\(x\) = 53 + 3.4.7
6\(x\) = 125 + 12.7
6\(x\) = 125 + 84
6\(x\) = 209
\(x\) = 209 : 6
\(x\) = \(\dfrac{209}{6}\)
b; 11\(x\) - 7\(x\) + 34 : 33 = 54 + 2\(x\)
4\(x\) + 3 = 625 + 2\(x\)
4\(x\) - 2\(x\) = 625 - 3
2\(x\) = 622
\(x\) = 622 : 2
\(x\) = 311
c; 75 - 5.(\(x-3\))3 = 700
5.(\(x\) - 3)3 = 700 - 75
5.(\(x\) - 3)3 = - 625
(\(x\) - 30)3 = - 625 : 5
(\(x\) - 30)3 = - 125
(\(x-3\))3 = (-5)3
\(x\) - 3 = - 5
\(x\) = - 5 + 3
\(x\) = -2
d, 3.(2\(x\) - 1)2 = 75
(2\(x\) - 1)2 = 75 : 3
(2\(x\) - 1)2 = 25
\(\left[{}\begin{matrix}2x-1=-5\\2x-1=5\end{matrix}\right.\)
\(\left[{}\begin{matrix}2x=-5+1\\2x=5+1\end{matrix}\right.\)
\(\left[{}\begin{matrix}2x=-4\\2x=6\end{matrix}\right.\)
\(\left[{}\begin{matrix}x=-2\\x=3\end{matrix}\right.\)
d) \(3.\left(2x-1\right)^2=75\)
\(\left(2x-1\right)^2=75\div3\)
\(\left(2x-1\right)^2=25\)
\(\left(2x-1\right)^2=5^2\)
\(\Rightarrow2x-1=5\)
\(2x=5+1\)
\(2x=6\)
\(x=6\div2\)
\(x=3\)
e, 3\(x\) + 3\(x\) + 2 = 270
2.3\(x\) = 270 - 2
2.3\(^x\) = 268
3\(^x\) = 268 : 2
3\(^x\) = 134
3\(x\) là số lẻ ≠ 134 là số chẵn với mọi \(x\) nguyên
Vậy không có giá trị nào của \(x\) thỏa mãn yêu cầu đề bài.
trường hợp
e; 3\(^x\) + 3\(^{x+2}\) = 270
3\(^x\) .( 1 + 32) = 270
3\(^x\) . 10 = 270
3\(^x\) = 270 : 10
3\(^x\) = 27
3\(^x\) = 33
\(x\) = 3
f; 3\(x\)-3 - 3\(^2\) = 2.32
3\(^{x-3}\) = 2.32 + 32
3\(^{x-3}\) = 32.(2 + 1)
3\(^{x-3}\) = 32.3
3\(^{x-3}\) = 33
\(x\) - 3 = 3
\(x\) = 3 + 3
\(x\) = 6
