Question

TÌM x

\(3^x+3^{x+2}=9^{17}+27^{12}\)

Answer 1

\(x\in z\) NHA MỌI NGƯỜI

Answer 2

\(3^x+3^{x+2}=9^{17}+27^{12}\)

\(\Leftrightarrow3^x+3^x.3^2=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)

\(\Leftrightarrow3^x\left(1+3^2\right)=3^{34}+3^{36}\)

\(\Leftrightarrow3^x\left(1+3^2\right)=3^{34}\left(1+3^2\right)\)

\(\Leftrightarrow3^x=3^{34}\) ( Chia cả hai vế cho \(1+3^2\) )

\(\Leftrightarrow x=34\)

Vậy : \(x=34\)

Answer 3

\(3^x+3^{x+2}=9^{17}+27^{12}\)

\(3^x+3^x.3^2=\left(3^2\right)^{17}+\left(3^3\right)^{12}\)

\(3^x.\left(1+3^2\right)=3^{34}+3^{36}\)

\(3^x.\left(1+3^2\right)=3^{34}\left(1+3^2\right)\)

\(\Rightarrow3^x=3^{34}\)

\(\Rightarrow x=34\)

Answer 4

\(3^x+3^{x+2}=9^{17}+27^{12}\)

\(3^x\left(1+3^2\right)=3^{34}+3^{36}\)

\(3^x\left(1+3^2\right)=3^{34}\left(1+3^2\right)\)

\(3^x=3^{34}\Rightarrow x=34\)

Answer 5

\(3^x+3^{x+2}=9^{17}+27^{12}\)

\(3^x\left(1+3^2\right)=3^{34}+3^{36}\)

\(=3^x\left(1+3^2\right)=3^{34}\left(1+3^2\right)\)

\(3^x=3^{34}\)

\(\Leftrightarrow x=34\)