Question

Tìm x biết

( 1 phần 2 ) mũ x = (1 phần 8 ) mũ x -2

help me . thaks

Answer 1

\(\left(\dfrac{1}{2}\right)^x=\left(\dfrac{1}{8}\right)^{x-2}\)

\(\Leftrightarrow\left(\dfrac{1}{2}\right)^x=\left(\dfrac{1}{2}\right)^{3x-6}\)

\(\Leftrightarrow x=3x-6\)

\(\Leftrightarrow3x-x=6\)

\(\Leftrightarrow2x=6\)

\(\Leftrightarrow x=3\left(tm\right)\)

Vậy ........

Answer 2

\(\left(\dfrac{1}{2}\right)^x=\left(\dfrac{1}{8}\right)^{x-2}\\ \Rightarrow\left(\dfrac{1}{2}\right)^x=\left(\dfrac{1^3}{2^3}\right)^{x-2}\\ \Rightarrow\left(\dfrac{1}{2}\right)^x=\left(\dfrac{1}{2}\right)^{3\left(x-2\right)}\\ \Leftrightarrow3\left(x-2\right)=x\\ \Rightarrow3x-6=x\\ \Rightarrow3x-x=6\\ \Rightarrow x\left(3-1\right)=6\\ \Rightarrow2x=6\\ \Rightarrow x=6:2=3\)