a) \(5^4:\left(2x-1\right)^2=25\\ \Leftrightarrow5^4:\left(2x-1\right)^2=5^2\\ \Leftrightarrow5^4:5^2=\left(2x-1\right)^2\\ \Leftrightarrow\left[{}\begin{matrix}\left(2x-1\right)^2=5^2\\\left(2x-1\right)^2=\left(-5\right)^2\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}2x-1=5\\2x-1=-5\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-2\end{matrix}\right.\)
b) \(17^3.x=17^4\\ \Rightarrow x=17^4:17^3=17\)
c) \(\left(2x+1\right)^3:49=7\\ \Leftrightarrow\left(2x-1\right)^3:7^2=7\\ \Leftrightarrow\left(2x-1\right)^3=7.7^2=7^3\\ \Leftrightarrow2x-1=7\\ \Leftrightarrow x=4\)
a)54 : (2x - 1)2 =25
54 : (2x - 1)2 =52
(2x - 1)2 =54 : 52
(2x - 1)2 = 52
2x - 1 = 5
2x = 5+1
2x = 6
x = 6: 2
x = 3
b)173.x = 174
x = 174 : 173
x = 17
c)(2x + 1)3 : 49 =7
(2x + 1)3 = 7 . 49
(2x + 1)3 = 343
(2x + 1)3 = 73
2x +1 = 7
2x = 7- 1
2x = 6
x = 6:2
x = 3
a) 54 : (2x - 1)2 = 25
625 : (2x - 1)2 = 25
(2x - 1)2 = 625 : 25
(2x - 1)2 = 25
(2x - 1)2 = 52
(2x - 1) = 5
2x = 5 + 1
2x = 6
x = 6 : 2
x = 3
b) 173 . x = 174
x = 174 : 173
x = 171
x = 17
c) (2x + 1)3 : 49 = 7
(2x + 1)3 = 7 . 49
(2x + 1)3 = 343
(2x + 1)3 = 73
(2x + 1) = 7
2x = 7 - 1
2x = 6
x = 6 : 2
x = 3
b) 32, 33, 34 , 35.