\(\frac{-3^x.3^6}{-27.9^x}=-3\)

=\(\frac{-1^x.\left(-3^3\right)^2}{-27.3^x}=3\)

=\(\frac{-1^x.\left(-27\right)^2}{-27.3^x}=3\)

\(=\frac{-1^x.27}{-1.3^x}=3\)

\(=\frac{-27^x}{-3^x}=3\)

\(=\left(\frac{-27}{-3}\right)^x=3\)

Bạn lm tiếp nhé !!

\(A=1+3+3^2+...+3^{100}\)

\(\Rightarrow3A=3+3^2+3^3+...+3^{101}\)

\(\Rightarrow3A-A=3^{101}-1\)

\(\Rightarrow A=\frac{3^{101}-1}{2}\)

Theo đề bài suy ra \(\hept{\begin{cases}\frac{A}{3}=\frac{B}{1}\\\frac{B}{1}=\frac{C}{2}\end{cases}}\Rightarrow\frac{A}{3}=\frac{B}{1}=\frac{C}{2}\)

Áp dụng tính chất dãy tỉ số bằng nhau: \(\frac{\widehat{A}}{3}=\frac{\widehat{B}}{1}=\frac{\widehat{C}}{2}=\frac{\widehat{A}+\widehat{B}+\widehat{C}}{3+1+2}=\frac{180^o}{6}=30^o\)

Suy ra...

a) \(8< 2^x\le2^9.2^{-5}\)

\(\Leftrightarrow2^3< x\le2^{9-5}\)

\(\Leftrightarrow2^3< 2^x\le2^4\)

\(\Leftrightarrow3< x\le4\Leftrightarrow x=4\)

b) \(27< 81^3:3^x< 243\)

\(\Leftrightarrow3^2< \left(3^4\right)^3:3^x< 3^5\)

\(\Leftrightarrow3^2< 3^{12}:3^x< 3^5\)

\(\Leftrightarrow3^2< 3^{12-x}< 3^5\)

\(\Leftrightarrow2< 12-x< 5\)

\(\Leftrightarrow\hept{\begin{cases}x=8\\x=9\end{cases}}\)