\(\frac{3^{-m}}{81}=27\)

\(\frac{3^{-m}}{3^4}=3^3\)

\(3^{-m}=3^3\times3^4\)

\(3^{-m}=3^7\)

\(-m=7\)

\(m=7\)

3^-m  = 3⁷

1/3^m = 3⁷

3^{m +7} = 1 = 3^o

m= -7

tài năng toán học đặng yến linh

(3^-m)/81=27

=>3^-m=2187                 Mà 2187=3^7

=>3^-m=3^7

=>-m = 7

=>m=-7

\(\frac{3^{-m}}{81}=27\)

\(\Rightarrow3^{-m}=27.81\)

\(\Rightarrow3^{-m}=2187\)

Vì nếu k^-m  thì =>k=\(\frac{1}{k^m}\)

Mà 2187 \(\in\)N

=>ko tìm đc

\(\frac{3^{-m}}{81}=27\)

\(3^{-m}=27.81\)

\(3^{-m}=3^3.3^4\)

\(3^{-m}=3^{3+4}=3^7\)

\(\Rightarrow-m=7\)

\(\Rightarrow m=-7\)

Vậy \(m=-7\)

\(\Leftrightarrow3^{-m}=27.81=3^3.3^4=3^7\)

\(\Leftrightarrow-m=7\Rightarrow m=-7\)

Vậy \(m=-7\)

\(\frac{3^{-m}}{81}=27\)

\(\Leftrightarrow\left(3^{-m}\right)=27.81\)

\(\Leftrightarrow3^{-m}=3^7\)

\(\Leftrightarrow-m=-7\)

\(\Rightarrow m=7\)

Vậy m= 7

\(M=\frac{3^6.3^8.5^4-3^{15}.5^{13-9}}{3^{12}.5^6+3^{18}.5^9}.2.\frac{25}{9}=\frac{3^{14}.5^4\left(1-3\right).2.5^2}{3^{12}.5^6\left(1+3^6.5^3\right).3^2}=\frac{-4}{1+3^6.5^3}\)

haizzz

\(m:3+m:9+m:27+m:81=\frac{5}{9}\)

\(m:\left(3+9+27+81\right)=\frac{5}{9}\)

\(m:120=\frac{5}{9}\)

\(m=\frac{5}{9}\times120\)

\(m=\frac{200}{3}\)

\(m.\frac{1}{3}+m.\frac{1}{9}+m.\frac{1}{27}+m.\frac{1}{81}=\frac{5}{9}\)

\(m\left(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}\right)=\frac{5}{9}\)

Vì: \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}=\frac{27}{81}+\frac{9}{81}+\frac{3}{81}+\frac{1}{81}=\frac{40}{81}\)

nên \(m.\frac{40}{81}=\frac{5}{9}\)

\(m=\frac{5}{9}:\frac{40}{81}=\frac{5}{9}.\frac{81}{40}=\frac{9}{8}\)

1. \(\frac{x^7}{81}=27\Leftrightarrow x^7=2187\)

\(\Leftrightarrow x^7=3^7\Leftrightarrow x=3\)

2. \(\left(x^4\right)^2=\frac{x^{12}}{x^5}\Leftrightarrow x^8=x^7\)

\(\Leftrightarrow x^8-x^7=0\Leftrightarrow x^7\left(x-1\right)=0\)

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

Vậy,...

3.\(x^{10}=25x^8\Leftrightarrow x^{10}-25x^8=0\)

\(\Leftrightarrow x^8\left(x^2-25\right)=0\Leftrightarrow x^8\left(x+5\right)\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^8=0\\x+5=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-5\\x=5\end{matrix}\right.\)

4. \(\left(3x-1\right)^3=\frac{-8}{27}\Leftrightarrow\left(3x-1\right)^3=\left(\frac{-2}{3}\right)^3\)

\(\Leftrightarrow3x-1=\frac{-2}{3}\Leftrightarrow3x=\frac{1}{3}\)

\(\Leftrightarrow x=\frac{1}{9}\)