Question

Tìm x:

\(1-\frac{2}{3}\left|x\right|=\frac{1}{2}\)

\(\left|\frac{2}{3}x+1\right|=\frac{1}{3}\)

2^x+2^x+1=48

3^x+1+3^x=108

Answer 1

a) 1 - \(\frac{2}{3}\)|x| = \(\frac{1}{2}\)

=> \(\frac{2}{3}\)|x| = \(\frac{1}{2}\)

=> |x| = \(\frac{1}{2}\) : \(\frac{2}{3}\)

=> |x| = \(\frac{3}{4}\)

=> x = \(\frac{3}{4}\) hoặc x = \(\frac{-3}{4}\)

Vậy x = \(\frac{3}{4}\) hoặc x = \(\frac{-3}{4}\)

b) ∣\(\frac{2}{3}\)x+1∣ = \(\frac{1}{3}\) => \(\frac{2}{3}\)x+1 = \(\frac{1}{3}\) hoặc \(\frac{2}{3}\)x+1 = \(\frac{-1}{3}\) Với \(\frac{2}{3}\)x+1 = \(\frac{1}{3}\) => \(\frac{2}{3}\)x = \(\frac{-2}{3}\) => x = -1 Với \(\frac{2}{3}\)x+1 = \(\frac{-1}{3}\) => \(\frac{2}{3}\)x = \(\frac{-4}{3}\) => x = -2 Vậy x = -1 hoặc x = -2. c) 2^x + 2^{x + 1} = 48 => 2^x (1 + 2) = 48 => 2^x . 3 = 48 => 2^x = 48 : 3 => 2^x = 16 => 2^x = 2⁴ => x = 4 Vậy x = 4 d) 3^{x + 1} + 3^x = 108 => 3^x (3 + 1) = 108 => 3^x . 4 = 108 => 3^x = 108 : 4 => 3^x = 27 => 3^x = 3³ => x = 3 Vậy x = 3.