Question

Tìm x, biết:

a)3^x-2 +3^x=810

b)40224022³.(x²-1)=80448044³

c)2x+4x+6x+8x+.....+100x=7650.

Answer 1

a)\(3^{x-2}+3^x=810\)

\(\Leftrightarrow3^x\left(3^{-2}+1\right)=810\)

\(\Leftrightarrow3^x\cdot\frac{10}{9}=810\)

\(\Leftrightarrow3^x=729\)

\(\Leftrightarrow3^x=3^6\)

\(\Leftrightarrow x=6\)

 

Answer 2

b)40224022³.(x²-1)=80448044³

\(\Leftrightarrow x^2-1=80448044^3:40224022^3\)

\(\Leftrightarrow x^2-1=\left(\frac{80448044}{40224022}\right)^3\)

\(\Leftrightarrow x^2-1=2^3\)

\(\Leftrightarrow x^2=9\)

\(\Leftrightarrow x=\pm3\)

 

Answer 3

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:

\(x\cdot2550=7650\)

\(\Leftrightarrow x=3\)