Question

Giá trị của x thỏa mãn :

\(\left(\frac{1}{2}\right)^{-x+4}=\left(\frac{1}{4}\right)^{\frac{3}{2}x-4}\)

Answer 1

\(\left(\frac{1}{2}\right)^{-x+4}=\left(\frac{1}{4}\right)^{\frac{3}{2}x-4}\)

=>\(\left(\frac{1}{2}\right)^{-x+4}=\left(\frac{1}{2}\right)^{3x-8}\)

=>-x+4=3x-8

<=>4x=12

<=>x=3

Vậy x=3

Answer 2

\(\left(\frac{1}{4}\right)^{\frac{3}{2}-4}=\left(\frac{1}{2}\right)^{2.\left(\frac{3}{2}-4\right)}=\left(\frac{1}{2}\right)^{-1}\)

; do đó -x + 4 = -1

=> -x = -1 - 4 = -5

=> x = 5

Answer 3

<=> \(\left(\frac{1}{2}\right)^{-x+4}=\left(\frac{1}{2}\right)^{3x-4}< =>-x+4=3x-4< =>x=2\)

Answer 4

Sửa lại :

\(\left(\frac{1}{4}\right)^{\frac{3}{2}x-4}=\left(\frac{1}{2}\right)^{2.\left(\frac{3}{2}x-4\right)}=\left(\frac{1}{2}\right)^{3x-8}\)

nên -x + 4 = 3x - 8

=> 3x - (-x) = 12

<=> 4x = 12

<=> x = 3