Bài 1: Tìm n biết
a) -32 / -2^n= 4
\(-\frac{32}{-2^n}=4\Rightarrow\frac{32}{2^n}=4\Rightarrow4\cdot2^n=32\)
\(\Rightarrow2^n=8\Rightarrow2^n=2^3\Rightarrow n=3\)
b) ( 1/2 ) ^2n-1 = 1/8
Ta có : \(\left(\frac{1}{2}\right)^{2n-1}=\frac{1}{8}\)
mà \(\frac{1}{8}=\left(\frac{1}{2}\right)^3\)
\(\Rightarrow2n-1=3\)
\(\Rightarrow2n=4\)
\(\Rightarrow n=2\)
Bài 2:Tìm x
a)
\(\frac{x}{\frac{4}{2}}=\frac{4}{\frac{x}{2}}\Rightarrow\frac{x}{4}=\frac{4}{x}\)
\(\Rightarrow x^2=4\cdot4\)
\(\Rightarrow x^2=16\)
mà 16=42=(-4)2
\(\Rightarrow\orbr{\begin{cases}x=4\\x=-4\end{cases}}\)
Vậy \(x\in\left\{4;-4\right\}\)
b) (x+5)^3 = -64
Vì (x+5)3 = -64
mà -64=(-4)3
\(\Rightarrow x+5=-4\)
\(\Rightarrow x=1\)
c) (2x-3)^2 = 9
\(\Rightarrow\orbr{\begin{cases}2x-3=3\\2x-3=-3\end{cases}\Rightarrow\orbr{\begin{cases}2x=6\\2x=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=3\\x=0\end{cases}}}\)
Vậy \(x\in\left\{3;0\right\}\)
