Question

Tìm số nguyên x,nếu biết:
\(\dfrac{2^{2x-3}}{4^{10}}\)= 8³x16⁵

Answer 1

\(\Leftrightarrow2^{2x-3}=2^9\cdot2^{20}\cdot2^{20}=2^{49}\)

=>2x-3=49

hay x=26

Answer 2

\(\dfrac{2^{2x-3}}{4^{10}}=8^3.16^5\)
\(\Leftrightarrow2^{2x-3}=\left(2^3\right)^3.\left(2^4\right)^5.\left(2^2\right)^{10}\)
\(\Rightarrow2^{2x-3}=2^9.2^{20}.2^{20}\)
\(\Rightarrow\)\(2^{2x-3}=2^{49}\)
\(\Rightarrow2x-3=49\)
\(\Rightarrow2x=52\)
\(\Rightarrow x=26\)