Question

Cho biểu thức M = \(6\) + \(6^2+6^3+...+6^{2021}\), tìm x thỏa mãn 5M + 6 = \(6^x\)

Answer 1

\(M=6+6^2+6^3+...+6^{2021}\)

\(\Rightarrow6M=6^2+6^3+6^4+...+6^{2022}\)

\(\Rightarrow6M-M=6^2+6^3+6^4+...+6^{2022}-\left(6+6^2+6^3+...+6^{2021}\right)\)

\(\Rightarrow5M=6^{2022}-6\)

\(\Rightarrow M=\dfrac{6^{2022}-6}{5}\)

\(5M+6=6^x\)

\(\Rightarrow5.\dfrac{6^{2022}-6}{5}+6=6^x\)

\(\Rightarrow6^{2022}-6+6=6^x\)

\(\Rightarrow6^{2022}=6^x\)

\(\Rightarrow x=2022\)