Question

Tìm \(x;\)biết:

\(3^x+3^{x+1}+3^{x+2}=117\)

Answer 1

\(3^x+3^{x+1}+3^{x+2}=117\)

\(\Rightarrow3^x+3^x.3+3^x.9=117\)

\(\Rightarrow3^x.\left(1+3+9\right)=117\)

\(\Rightarrow3^x.13=117\)

\(\Rightarrow3^x=117:13\)

\(\Rightarrow3^x=9\)

\(\Rightarrow3^x=3^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

Answer 2

\(3^x+3^{x+1}+3^{x+2}=117\)

\(\Rightarrow3^x+3^x.3+3^x.9=117\)

\(\Rightarrow3^x.\left(1+3+9\right)=117\)

\(\Rightarrow3^x=117:13\)

\(\Rightarrow3^x=9\)

\(\Leftrightarrow3^x=3^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

Answer 3

\(3^x+3^{x+1}+3^{x+2}=117\)

=> \(3^x\left(1+3+3^2\right)=117\)

=> \(3^x.13=117\)

=> \(3^x=9\)

mà \(9=3^2\)

=> x = 2

Answer 4

3 x + 3 x+1 + 3 x+2 = 117

3 x + 3 x .3 + 3 x .9 = 117

3 x .(1 + 3 + 9) = 117

3 x .13 = 117

3 x = 117 : 13

3 x = 9 ⇒ 3 x = 3 2

x = 2 x = 2