a)\(3^{x-2}+3^x=810\)
\(\Leftrightarrow3^x\left(3^{-2}+1\right)=810\)
\(\Leftrightarrow3^x\cdot\frac{10}{9}=810\)
\(\Leftrightarrow3^x=729\)
\(\Leftrightarrow3^x=3^6\)
\(\Leftrightarrow x=6\)
b)402240223.(x2-1)=804480443
\(\Leftrightarrow x^2-1=80448044^3:40224022^3\)
\(\Leftrightarrow x^2-1=\left(\frac{80448044}{40224022}\right)^3\)
\(\Leftrightarrow x^2-1=2^3\)
\(\Leftrightarrow x^2=9\)
\(\Leftrightarrow x=\pm3\)
c)2x+4x+6x+8x+.....+100x=7650.
\(\Leftrightarrow x\left(2+4+...+100\right)=7650\)
Đặt \(A=2+4+...+100\)
Tổng A có số số hạng là:
\(\left(100-2\right):2+1=50\)(số)
Tổng A là:
\(\left(100+2\right)\cdot50:2=2550\)
Thay A vào ta có:
\(x\cdot2550=7650\)
\(\Leftrightarrow x=3\)