Question

[Hoàng Rin]

Tìm x, biết :

1, (8x-1) ²ⁿ⁺¹ = 7²ⁿ⁺¹

2, 5^x. (5^{3)2 = 625}

^3, (x-7)^x+1 -(x-7)^x+11=0

4, 2.16 > 2^x> 4 (x € N)

5, 9.27 < 3^x < 24³ ( x € N )

Answer 1

[Nguyễn Thanh Hằng]

a) Ta có :

\(\left(8x-1\right)^{2n+1}=7^{2n+1}\)

\(\Leftrightarrow8x-1=7\)

\(\Leftrightarrow8x=8\)

\(\Leftrightarrow x=1\left(tm\right)\)

Vạy ..........

2) \(5^x.\left(5^3\right)^2=625\)

\(\Leftrightarrow5^x.5^6=625\)

\(\Leftrightarrow5^{x+6}=5^4\)

\(\Leftrightarrow x+6=4\)

\(\Leftrightarrow x=-2\left(tm\right)\)

Vậy ...............

3) \(\left(x-7\right)^{x+1}-\left(x-7\right)^{x+11}=0\)

\(\Leftrightarrow\left(x-7\right)^{x+1}.\left[1-\left(x-7\right)^{10}\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\\left(x-7\right)^{10}=1\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\\left[{}\begin{matrix}x-7=1\\x-7=-1\end{matrix}\right.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=7\\\left[{}\begin{matrix}x=8\\x=6\end{matrix}\right.\end{matrix}\right.\)

Vậy ..

Answer 2

[Phạm Ánh Tuyết]

1,(8x-1)²ⁿ⁺¹=7²ⁿ⁺¹

^=>8x-1=7

^=>8x=8

^=>x=1

^{Vậy x=1}