Question

[Nguyễn Tạ Hoàng Hải]

giúp mn đi mn mình tick cho

tìm x:

                14 . 7²⁰²¹  = 35 . 7²⁰²¹ - 3 . 49^x

Answer 1

[Toru]

\(14\cdot7^{2021}=35\cdot7^{2021}-3\cdot49^x\)

\(\Rightarrow35\cdot7^{2021}-3\cdot49^x=14\cdot7^{2021}\)

\(\Rightarrow5\cdot7\cdot7^{2021}-3\cdot\left(7^2\right)^x=2\cdot7\cdot7^{2021}\)

\(\Rightarrow5\cdot7^{2022}-3\cdot7^{2x}=2\cdot7^{2022}\)

\(\Rightarrow3\cdot7^{2x}=5\cdot7^{2022}-2\cdot7^{2022}\)

\(\Rightarrow3\cdot7^{2x}=\left(5-2\right)\cdot7^{2022}\)

\(\Rightarrow3\cdot7^{2x}=3\cdot7^{2022}\)

\(\Rightarrow7^{2x}=7^{2022}\)

\(\Rightarrow2x=2022\)

\(\Rightarrow x=2022:2\)

\(\Rightarrow x=1011\)

Vậy \(x=1011\).