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.

1) 3 * 9^x = 81

3 * (3²)^x = 81

3 * 3^2x = 81

3^2x+1 = 81

3^2x+1 = 3⁴

2x + 1 = 4

2x = 3

x = 3/2

x = 1,5

2) 2 * 4^x = 64

4^x = 32

(2²)^x = 2⁵

2^2x = 2⁵

2x = 5

x = 5/2

x = 2,5

3) 3^(x+1)/2 * 3^x-2 = 1

3^{(x+1)/2 + x - 2} = 1

3^{(x+1)/2 + x - 2} = 3⁰

(x+1)/2 + x - 2 = 0

x/2 + 1/2 + x - 2 = 0

3x/2 = 3/2

x = 1

4) 0,5^x+7 * 0,5^1-2x = 2

0,5^{x+7 + 1 - 2x} = 2

0,5^8-x = 2

(1/2)^8-x = 2

2^-8+x = 2¹

-8 + x = 1

x = 9

5) 0,6^x * 0,6³ = 0,6^2x / 0,6⁵

0,6^x+3 = 0,6^2x-5

x + 3 = 2x - 5

x = 8

6) 6^3x * (1/6) = 6 * (1/6)^2x

6^3x * 6⁻¹ = 6 * 6^-2x

6^{3x - 1} = 6^1-2x

3x - 1 = 1 - 2x

5x = 2

x = 2/5

x = 0,4

Ответ: 1) x = 1,5; 2) x = 2,5; 3) x = 1; 4) x = 9; 5) x = 8; 6) x = 0,4