Question

tìm x thuộc N sao cho 3^x+2.3^x-2=297

thank

 

Answer 1

\(3^x+2.3^{x-2}=297\)

\(\Rightarrow3^x\left(1+2.3^{-2}\right)=297\)

\(\Rightarrow3^x\left(1+2.\dfrac{1}{3^2}\right)=297\)

\(\Rightarrow3^x\left(1+\dfrac{2}{9}\right)=297\)

\(\Rightarrow3^x\left(\dfrac{9}{9}+\dfrac{2}{9}\right)=297\)

\(\Rightarrow3^x.\dfrac{11}{9}=297\)

\(\Rightarrow3^x=297:\dfrac{11}{9}=297.\dfrac{9}{11}=243\)

\(\Rightarrow3^x=3^5\)

\(\Rightarrow x=5\) (thỏa mãn)

Answer 2

\(3^x+2.3^{x-2}=297\)

\(3^x+2.3^x:3^2=297\)

\(3^x\left(1+\dfrac{2}{9}\right)=297\)

\(3^x.\dfrac{11}{9}=297\)

\(3^x=297:\dfrac{11}{9}=243=3^5\)

⇒\(x=5\)