Ta có :\(\frac{3^2.3^8}{27^3}=3^x\)

\(\Rightarrow\frac{3^{10}}{\left(3^3\right)^3}=3^x\)

\(\Rightarrow\frac{3^{10}}{3^9}=3^x\)

\(\Rightarrow3^1=3^x\)

\(\Rightarrow x=1\)

Vậy \(x=1\)

\(\frac{3^2.3^8}{27^3}\)=\(\frac{3^{10}}{27^3}\)=\(\frac{3^{10}}{\left(3^3\right)^3}\)=\(\frac{3^{10}}{3^9}\)=3

Mà \(\frac{3^2.3^8}{27^3}\)=3^x

\(\Rightarrow\)3=3^x

\(\Rightarrow\)x=1

Vậy x=1.

\(\frac{3^2.3^8}{27^3}=3^x\)

\(\Leftrightarrow\frac{3^{2+8}}{\left(3^3\right)^3}=3^x\)

\(\Leftrightarrow\frac{3^{10}}{3^9}=3^x\)

\(\Leftrightarrow3=3^x\)

\(\Leftrightarrow x=1\)

           \(\frac{3^2.3^8}{27^3}=3^x\)

<=>    \(\frac{3^{10}}{3^9}=3^x\)

<=>     \(3=3^x\)

<=>      x=1

\(\frac{3^2\cdot3^8}{27^3}=3^x\)

\(\Leftrightarrow3^2\cdot3^8=27^3\cdot3^x\)

\(\Leftrightarrow3^{10}=\left(3^3\right)^3\cdot3^x\)

\(\Leftrightarrow3^{10}=3^9\cdot3^x\)

\(\Leftrightarrow3^{10}=3^{9+x}\)

\(\Rightarrow10=9+x\)

\(\Leftrightarrow x=1\)

\(\frac{3^2.3^8}{\left(3^3\right)^3}=3^x\frac{3^{10}}{3^9}=3^x3^{10-9}=3^x3^x=3x=1\)

\(\Rightarrow\frac{3^2.3^8}{3.3^8}=3^x\Rightarrow3=3^x\Rightarrow x=1\)

a)\(\left(-3\right)^{x+3}=-\frac{1}{27}\)

\(\left(-3\right)^{x+3}=\left(-\frac{1}{3}\right)^3\)

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

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

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

\(\Rightarrow x+3=-3\)

\(\Rightarrow x=-6\)

b)\(\left(-6\right)^{2x+2}=\frac{1}{36}\)

\(\left(-6\right)^{2x+2}=\left(-\frac{1}{6}\right)^2\)

\(\left(-6\right)^{2x+2}=\left(-\frac{6^0}{6^1}\right)^2\)

\(\left(-6\right)^{2x+2}=\left(-6^{-1}\right)^2\)

\(\left(-6\right)^{2x+2}=\left(-6\right)^{-2}\)

\(\Rightarrow2x+2=-2\)

\(\Rightarrow2x=-4\)

\(\Rightarrow x=-2\)

c)\(\left(-3\right)^{x+5}=\frac{1}{81}\)

\(\left(-3\right)^{x+5}=\left(-\frac{1}{3}\right)^4\)

\(\left(-3\right)^{x+5}=\left(-\frac{3^0}{3^1}\right)^4\)

\(\left(-3\right)^{x+5}=\left(-3^{-1}\right)^4\)

\(\left(-3\right)^{x+5}=\left(-3\right)^{-4}\)

\(\Rightarrow x+5=-4\)

\(\Rightarrow x=-9\)

d)\(\left(\frac{1}{9}\right)^x=\left(\frac{1}{27}\right)^6\)

\(\left[\left(\frac{1}{3}\right)^2\right]^x=\left[\left(\frac{1}{3}\right)^3\right]^6\)

\(\left(\frac{1}{3}\right)^{2x}=\left(\frac{1}{3}\right)^{18}\)

\(\Rightarrow2x=18\)

\(\Rightarrow x=9\)

e)\(\left(\frac{4}{9}\right)^x=\left(\frac{8}{27}\right)^6\)

\(\left[\left(\frac{2}{3}\right)^2\right]^x=\left[\left(\frac{2}{3}\right)^3\right]^6\)

\(\left(\frac{2}{3}\right)^{2x}=\left(\frac{2}{3}\right)^{18}\)

\(\Rightarrow2x=18\)

\(\Rightarrow x=9\)

f)\(5^{x+4}-3\cdot5^{x+3}=2\cdot5^{11}\)

\(5^{x+3}\cdot5-3\cdot5^{x+3}=2\cdot5^{11}\)

\(5^{x+3}\left(5-3\right)=2\cdot5^{11}\)

\(5^{x+3}\cdot2=2\cdot5^{11}\)

\(\Rightarrow5^{x+3}=5^{11}\)

\(\Rightarrow x+3=11\)

\(\Rightarrow x=8\)

r)\(4\cdot3^{x-1}+2\cdot3^{x+2}=4\cdot3^6+2\cdot3^9\)

\(4\cdot3^x:3+2\cdot3^x\cdot9=4.3^7:3+2\cdot3^7\cdot9\)

\(3^x\left(4:3+2\cdot9\right)=3^7\left(4:3+2\cdot9\right)\)

\(\Rightarrow3^x=3^7\)

\(\Rightarrow x=7\)

Help me plsss

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Số to quá chịu :(

\(\dfrac{3^2.3^8}{27^3}\)

\(=\dfrac{3^2.3^8}{\left(3^3\right)^3}\)

\(=\dfrac{3^2.3^8}{3^9}\)

\(=\dfrac{3^{10}}{3^9}\)

\(=3^1=3\)

\(3=3x\)

\(x=3:3\)

\(x=1\)

a)

\(\text{( 25 – 2x )³ : 5 – 3^2 = 4^2}\)

\(\text{( 25 – 2x )³ : 5 – 9 = 16}\)

\(\text{( 25 – 2x )³ : 5 = 16 + 9}\)

\(\text{( 25 – 2x )³ : 5 = 25}\)

\(\text{( 25 – 2x )³ = 25 . 5}\)

\(\text{( 25 – 2x )³ = 125}\)

\(\text{( 25 – 2x )³ = 5³}\)

\(\text{25 – 2x = 5}\)

\(\text{2x = 25 – 5}\)

\(\text{2x = 20}\)

\(\text{x = 10}\)

\(\text{________________________________________}\)

b)

\(\text{2.3^x = 10.3^12 + 8.27^4}\)

\(\text{2.3^x = 10.3^12 + 8.(3^3)^4}\)

\(\text{2.3^x = 3^12 . (10+8)}\)

\(\text{2.3^x = 3^12 . 18}\)

\(\text{3^x = 3^12 . 18:2}\)

\(\text{3^x = 3^12 . 9}\)

\(\text{3^x = 3^12 . 3^2}\)

\(\text{3^x = 3^14}\)

\(\text{=> x=14}\)

\(2.3^x=10.3^{12}+8.27^4\\ \Rightarrow2.3^x=10.3^{12}+8.\left(3^3\right)^4\\ \Rightarrow2.3^x=10.3^{12}+8.3^{12}\\ \Rightarrow2.3^x=3^{12}\left(10+8\right)\\ \Rightarrow2.3^x=3^{12}.18\)

\(=>3^x=3^{12}.18:2\\ \Rightarrow3^x=3^{12}.3^2\\ \Rightarrow3^x=3^{10}\)

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