Question

Tìm x:

2^x+9-2^x+8-2^x+7-...............-2^x+1-2^x=1024

Tính:

A=\(\dfrac{125.4^2.\left(2^{15}\right)^3}{13.2^{13}.8^6-64^5}\)

Answer 1

\(2^{x+9}-2^{x+8}-2^{x+7}-..........-2^{x+1}-2^x=1024\)

\(\Leftrightarrow2^x.2^9-2^x.2^8-.........-2^x.2-2^x=1024\)

\(\Leftrightarrow2^x\left(2^9-2^8-.........-2-1\right)=1024\)

Đặt :

\(A=2^9-2^8-......-2-1\Leftrightarrow2^x.A=1024\)

\(\Leftrightarrow A=2^9-\left(2^8+2^7+........+2+1\right)\)

\(\Leftrightarrow A=2^9-\left(2^9-1\right)\)

\(\Leftrightarrow A=1\)

\(\Leftrightarrow2^x.1=1024\)

\(\Leftrightarrow2^x=2^{10}\)

\(\Leftrightarrow x=10\)

Vậy ...