Question

Tìm x biết:

a) 3\(^{x-2}\)= 27 . 9

b) 2\(^{x+1}\)+ 2\(^{x+3}\)= 80

c) 2\(^{2x-3}\)= 16 . 8

d) 2\(^{x-2}\) . 2\(^x\)= 64

Answer 1

a) \(3^{x-2}=27\cdot9\)

\(3^{x-2}=3^3\cdot3^2=3^5\)

\(\Rightarrow\)\(x-2=5\Rightarrow x=7\)

b) \(2^{x+1}+2^{x+3}=80\)

\(\Rightarrow2^{x+1}\left(1+2^2\right)=80\)

\(\Rightarrow2^{x+1}\cdot5=80\)

\(\Rightarrow2^{x+1}=16=2^4\)

\(\Rightarrow x+1=4\Rightarrow x=3\)

c) \(2^{2x-3}=16\cdot8\)

\(2^{2x-3}=2^4\cdot2^3=2^7\)

\(\Rightarrow2x-3=7\)

\(\Rightarrow2x=4\Rightarrow x=2\)

d) \(2^{x-2}\cdot2^x=64\)

\(\Rightarrow2^{x-2+x}=64=2^6\)

\(\Rightarrow x-2+x=6\)

\(\Rightarrow2x-2=6\)

\(\Rightarrow2x=8\Rightarrow x=4\)

Answer 2

Giải:

a) \(3^{x-2}=27.9\)

\(\Leftrightarrow3^{x-2}=3^3.3^2\)

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

Vì \(3=3\)

Nên \(x-2=5\)

\(\Leftrightarrow x=5+2\)

\(\Leftrightarrow x=7\)

Vậy x = 7.

b) \(2^{x+1}+2^{x+3}=80\)

\(\Leftrightarrow2^{x+1}\left(1+2^2\right)=80\)

\(\Leftrightarrow2^{x+1}.5=80\)

\(\Leftrightarrow2^{x+1}=\dfrac{80}{5}=16\)

\(\Leftrightarrow2^{x+1}=2^4\)

Vì \(2=2\)

Nên \(x+1=4\)

\(\Leftrightarrow x=4-1\)

\(\Leftrightarrow x=3\)

Vậy x = 3.

c) \(2^{2x-3}=16.8\)

\(\Leftrightarrow2^{2x-3}=2^4.2^3\)

\(\Leftrightarrow2^{2x-3}=2^7\)

Vì \(2=2\)

Nên \(2x-3=7\)

\(\Leftrightarrow2x=7+3=10\)

\(\Leftrightarrow x=\dfrac{10}{2}=5\)

Vậy x = 5.

d) \(2^{x-2}.2^x=64\)

\(2^{2x-2}=2^6\)

Vì \(2=2\)

Nên \(2x-2=6\)

\(\Leftrightarrow2x=6+2=8\)

\(\Leftrightarrow x=\dfrac{8}{2}=4\)

Vậy x = 4.

Chúc bạn học tốt!