Đáp án + Giải thích các bước giải:
VD `2.4`
a, `(x - 3) : 2 = 5^14 : 5^12`
` (x - 3) : 2 = 25`
` x - 3 = 25 . 2`
` x - 3 = 50`
` x = 50 + 3`
` x = 53`
Vậy `x = 53`
b, `30 : (x - 7) = 15^19 : 15^18`
` 30 : (x - 7) = 15`
` x - 7 = 30 : 15`
` x - 7 = 2`
` x = 2 + 7`
` x = 9`
Vậy `x = 9`
c, `x^70 = x`
` x^70 - x = 0`
` x(x^69 - 1) = 0`
⇒\(\left[ \begin{array}{l}x=0\\x^{69}-1=0\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=0\\x^{69}=1\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=0\\x = 1\end{array} \right.\)
Vậy `x \in {0 ; 1}`
d, `(2x + 1)^3 = 9 . 81`
` (2x + 1)^3 = 9 . 9^2`
` (2x + 1)^3 = 9^3`
`=> 2x + 1 = 9`
`=> 2x = 9 - 1`
`=> 2x = 8`
`=> x = 4`
Vậy `x = 4`
e, `(4x - 1)^2 = 25 . 9`
` (4x - 1)^2 = 225`
` (4x - 1)^2 = 15^2 = (-15)^2`
⇒\(\left[ \begin{array}{l}4x-1=15\\4x-1=-15\end{array} \right.\)
⇒\(\left[ \begin{array}{l}4x=16\\4x=-14\end{array} \right.\)
⇒\(\left[ \begin{array}{l}x=4\\x= -\frac{7}{2}\end{array} \right.\)
Vì `x \in NN` nên `x = 4`
Vậy `x = 4`
