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МатематикаВопрос:
209 1) 27ˣ = 1/3; 2) 400ˣ = 1/20; 3) (1/5)ˣ = 25; 4) (1/3)ˣ = 1/81.
Ответ:
1) 27x = 1/3
(3³)x = 3⁻¹
33x = 3⁻¹
3x = -1
x = -1/3
2) 400x = 1/20
(20²)x = 20⁻¹
202x = 20⁻¹
2x = -1
x = -1/2
3) (1/5)x = 25
(5⁻¹)x = 5²
5-x = 5²
-x = 2
x = -2
4) (1/3)x = 1/81
(1/3)x = (1/3)⁴
x = 4
Ответ: 1) x = -1/3; 2) x = -1/2; 3) x = -2; 4) x = 4
Похожие
- 208 1) 4ˣ⁻¹ = 1; 2) 0,3³ˣ ⁻ ² = 1; 3) 2²ˣ = 2⁴√3; 4) (1/3)³ˣ = (1/3)⁻².
- 210 1) 3 ⋅ 9ˣ = 81; 2) 2 ⋅ 4ˣ = 64; 3) 3 ⁽ˣ⁺¹⁾/₂ ⋅ 3ˣ⁻² = 1; 4) 0,5ˣ⁺⁷ ⋅ 0,5¹⁻²ˣ = 2; 5) 0,6ˣ ⋅ 0,6³ = 0,6²ˣ / 0,6⁵; 6) 6³ˣ ⋅ 1/6 = 6 ⋅ (1/6)²ˣ.
- 211 1) 3²ˣ⁻¹ + 3²ˣ = 108; 2) 2³ˣ⁺² − 2³ˣ⁻² = 30; 3) 2ˣ⁺¹ + 2ˣ⁻¹ + 2ˣ = 28; 4) 3ˣ⁻¹ − 3ˣ + 3ˣ⁺¹ = 63.
- 212 1) 5ˣ = 8ˣ; 2) (1/2)ˣ = (1/3)ˣ; 3) 3ˣ = 5²ˣ; 4) 4ˣ = 32ˣ.
- 213 1) 9ˣ − 4 ⋅ 3ˣ + 3 = 0; 2) 16ˣ − 17 ⋅ 4ˣ + 16 = 0; 3) 25ˣ − 6 ⋅ 5ˣ + 5 = 0; 4) 64ˣ − 8ˣ − 56 = 0.
- 214 1) 3ˣ²⁺ˣ⁻¹² = 1; 2) 2ˣ²⁻⁷ˣ⁺¹⁰ = 1; 3) 2^(x-1)/(x-2) = 4; 4) 0,5ˣ = 4^(1/(x+1)).
