Question

[Yêu Isaac quá đi thui]

Tìm x :

( 4x -13 )\(^4\)+4\(^3\) = 145

3\(^{x+2}\)- \(3^x\)=72

\(2^{x+2}\)-\(2^{x-1}\)=224

hELp me !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

[Nguyễn Huy Tú]

a) \(\left(4x-13\right)^4+4^3=145\)

\(\Rightarrow\left(4x-13\right)^4+64=145\)

\(\Rightarrow\left(4x-13\right)^4=81\)

\(\Rightarrow4x-13=\pm3\)

+) \(4x-13=3\)

\(\Rightarrow4x=16\)

\(\Rightarrow x=4\)

+) \(4x-13=-3\)

\(\Rightarrow4x=10\)

\(\Rightarrow x=\frac{5}{2}\)

Vậy \(x=4\) hoặc \(x=\frac{5}{2}\)

b) \(3^{x+2}-3^x=72\)

\(\Rightarrow3^x.3^2-3^x=72\)

\(\Rightarrow3^x.\left(3^2-1\right)=72\)

\(\Rightarrow3^x.8=72\)

\(\Rightarrow3^x=9\)

\(\Rightarrow3^x=3^2\)

\(\Rightarrow x=2\)

Vậy \(x=2\)

c) \(2^{x+2}-2^{x-1}=224\)

\(\Rightarrow2^{x-1+3}-2^{x-1}=224\)

\(\Rightarrow2^{x-1}.2^3-2^{x-1}=224\)

\(\Rightarrow2^{x-1}.\left(2^3-1\right)=224\)

\(\Rightarrow2^{x-1}.7=224\)

\(\Rightarrow2^{x-1}=32\)

\(\Rightarrow2^{x-1}=2^5\)

\(\Rightarrow x-1=5\)

\(\Rightarrow x=6\)

Vậy x = 6

Answer 2

[Huỳnh Tâm]

(1) ↔ (4x - 3)⁴ = 81 ↔ (4x - 3)⁴ = 3⁴

↔ 4x - 3 = 3 hoặc 4x - 3 = -3 ↔ x = 3/2 hoặc x = 0

(2) ↔ 9*3^x - 3^x = 72 ↔ 8*3^x = 72 ↔ 3^x = 9 ↔ x = 2

(3) ↔ 8*2^x-1 - 2^x-1 = 224 ↔ 7*2^x-1 =224

↔ 2^x-1 = 32 ↔ x = 6