Question

2^2x+2^2x+1+2^2x+2+...+2^2x+1918=2¹⁹²³-2⁴

Answer 1

Đặt \(A=2^{2x}+2^{2x+1}+...+2^{2x+1918}\)

=>\(2\cdot A=2^{2x+1}+2^{2x+2}+...+2^{2x+1919}\)

=>\(A=2^{2x+1919}-2^{2x}\)

Theo đề, ta có; \(2^{2x+1919}-2^{2x}=2^{1923}-2^4\)

=>\(2^{2x}\cdot\left(2^{2019}-1\right)=2^4\left(2^{2019}-1\right)\)

=>2x=4

=>x=2