
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.


\(\left(\dfrac{1}{2}\right)^n=\left(\dfrac{1}{8}\right)^2\)
\(=>\left(\dfrac{1}{2}\right)^n=\left[\left(\dfrac{1}{2}\right)^3\right]^2\)
\(=>\left(\dfrac{1}{2}\right)^n=\left(\dfrac{1}{2}\right)^6\)
\(\Rightarrow n=6\)

\(\left(\dfrac{1}{4}\right)^{2n}=\left(\dfrac{1}{8}\right)^2\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{2.2n}=\left(\dfrac{1}{2}\right)^{3.2}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{4n}=\left(\dfrac{1}{2}\right)^6\)
\(\Rightarrow4n=6\)
\(\Rightarrow n=\dfrac{6}{4}=\dfrac{3}{2}\)

a) Vì \(-45< -16\) nên \(\left(-\dfrac{45}{17}\right)^{15}< \left(\dfrac{-16}{17}\right)^{15}\)
b) Vì \(21< 23\) nên \(\left(-\dfrac{8}{9}\right)^{21}< \left(-\dfrac{8}{9}\right)^{23}\)
c) \(27^{40}=3^{3^{40}}=3^{120}\)
\(64^{60}=8^{2^{60}}=8^{120}\)
Vì \(3< 8\) nên \(3^{120}< 8^{120}\) hay \(27^{40}< 64^{60}\)
con ai kooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooo

a, \(\frac{8}{2^n}=2\Rightarrow2.2^n=8\)
\(\Rightarrow2^{n+1}=2^3\)
\(\Rightarrow n+1=3\)
\(\Rightarrow n=2\)
d,\(\left(2n-3\right)^2=9\)
\(\left(2n-3\right)^2=3^2\)
\(\Rightarrow\orbr{\begin{cases}2n-3=-3\\2n-3=3\end{cases}\Rightarrow\orbr{\begin{cases}2n=-3+3\\2n=3+3\end{cases}\Rightarrow}\orbr{\begin{cases}2n=0\\2n=6\end{cases}\Rightarrow}\orbr{\begin{cases}n=0\\n=3\end{cases}}}\)
Vậy n=0; n= 3


\(\frac{\left(2^6\right)^2.\left(3^4\right)^3.34}{2^{13}.3^9.17}=\frac{2^{12}.3^{12}.2}{2^{13}.3^9}=3^3=27\)

Bài 5:
\(A+9=\frac{10}{1}+\frac{10}{2}+\frac{10}{3}+....+\frac{10}{9}\)
\(A=\frac{10}{2}+\frac{10}{2}+\frac{10}{3}+...+\frac{10}{9}+1=\frac{10}{2}+\frac{10}{3}+...+\frac{10}{9}+\frac{10}{10}\)
\(A=10\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{10}\right)=10B\)
$\Rightarrow A:B=10$

R(x)=x4+2x3-x2+x-3
Với x=1 ta có
R(x)=1+2-1+1-3=0
Với x=2 ta có
R(x)=16+16-4+2-3=27
Với x=-1 ta có
R(x)=1+(-2)-1+1-3=-4
Với x=0 ta có
R(x)=0+0-0+0-3=-3
Vậy chỉ có 1 là nghiệm cua R(x)

\(A=\frac{x^2-2x+1}{x+1}=\frac{x^2-2x-3+4}{x+1}=\frac{\left(x+1\right)\left(x-3\right)+4}{x+1}=x-3+\frac{4}{x+1}\inℤ\)
mà \(x\inℤ\)nên \(\frac{4}{x+1}\inℤ\)do đó \(x+1\inƯ\left(4\right)=\left\{-4,-2,-1,1,2,4\right\}\)
\(\Leftrightarrow x\in\left\{-5,-3,-2,0,1,3\right\}\).
sai đề bài rồi bạn
phải là:64/(-2^n)=8 chứ