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МатематикаВопрос:
212 1) 5ˣ = 8ˣ; 2) (1/2)ˣ = (1/3)ˣ; 3) 3ˣ = 5²ˣ; 4) 4ˣ = 32ˣ.
Ответ:
1) 5x = 8x
(5/8)x = 1
(5/8)x = (5/8)⁰
x = 0
2) (1/2)x = (1/3)x
(1/2)/(1/3) = 1
(3/2)x = 1
(3/2)x = (3/2)⁰
x = 0
3) 3x = 52x
3x = (5²)x
3x = 25x
(3/25)x = 1
(3/25)x = (3/25)⁰
x = 0
4) 4x = 32x
(4/32)x = 1
(1/8)x = 1
(1/8)x = (1/8)⁰
x = 0
Ответ: 1) x = 0; 2) x = 0; 3) x = 0; 4) x = 0
Похожие
- 208 1) 4ˣ⁻¹ = 1; 2) 0,3³ˣ ⁻ ² = 1; 3) 2²ˣ = 2⁴√3; 4) (1/3)³ˣ = (1/3)⁻².
- 209 1) 27ˣ = 1/3; 2) 400ˣ = 1/20; 3) (1/5)ˣ = 25; 4) (1/3)ˣ = 1/81.
- 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.
- 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)).
