Question

Să se rezolve ecuațiile:​

Answer 1

Răspuns:

Explicație pas cu pas:

a) (4/9)ˣ⁺¹ ·(27/8)ˣ = 2/3 <=>

(2/3)²ˣ⁺²·(3/2)ˣ = 2/3 <=>

(2/3)²ˣ⁺²·(2/3)⁻ˣ = 2/3 <=>

(2/3)²ˣ⁺²⁻ˣ = (2/3)¹ =>

x+2 = 1 => x = -1

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b) (3/11)³ˣ⁻¹⁰ = (11/3)⁷ˣ⁻¹⁰ <=>

(3/11)³ˣ⁻¹⁰ = (3/11)¹⁰⁻⁷ˣ =>

3x-10 = 10-7x => 10x = 20 => x = 2

Answer 2

Răspuns:

Explicație pas cu pas:

a)  (2/3) la puterea (2x+2) * (2/3^ la puterea (-3x) =2/3

(2/3)^(2x+2-3x)=(2/3) la puterea 1

2x+2-3x=1

x=1

a^m=a^n rezulta n=m

b) (3/11)^(3x-1)=(3/11)^10-7x

3x-1=10-7x

x=11/4