Question

Tìm x

 2\(^{^{ }-2}\).2\(^x\)+2.2\(^x\)=9.2\(^6\)

3\(^{-2}\).3\(^4\).3\(^x\)=3\(^7\)

 

Answer 1

3^-2 . 3⁴ . 3^x = 3⁷

<=> 3^{2 + x} = 3⁷

<=> 2 + x = 7

<=> x = 7 - 2

<=> x = 5

Answer 2

\(2^{-2}\cdot2^x+2\cdot2^x=9\cdot2^6\\ \Rightarrow2^{x-2}+2^{x+1}=9\cdot2^6\\ \Rightarrow2^{x-2}\left(1+2^3\right)=9\cdot2^6\\ \Rightarrow2^{x-2}\cdot9=9\cdot2^6\Rightarrow2^{x-2}=2^6\\ \Rightarrow x-2=6\Rightarrow x=8\)

\(3^{-2}\cdot3^4\cdot3^x=3^7\\ \Rightarrow3^{x+4-2}=3^7\\ \Rightarrow x+2=7\Rightarrow x=5\)

 

Answer 3

1) \(2^{-2}.2^x+2.2^x=9.2^6\)

\(\Rightarrow2^x.\left(2^{-2}+2\right)=576\)

\(\Rightarrow2^x.\dfrac{9}{4}=576\)

\(\Rightarrow2^x=256=2^8\Rightarrow x=8\)

2) \(\Rightarrow3^{x+2}=3^7\Rightarrow x+2=7\Rightarrow x=5\)

Answer 4

3^-2 . 3⁴ . 3^x = 3⁷

<=> 3^{2 + x} = 3⁷

<=> 2 + x = 7

<=> x = 7 - 2

<=> x = 5