(12,5)^0,25*(18,75)^0,75=(x/20)^0,25*(3x/80)^0,75

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вопрос

To solve this equation, we need to simplify each side separately and then solve for x:

On the left side:
(12,5)^0,25 = √12,5 ≈ 3,54
(18,75)^0,75 = √√18,75 ≈ 4,33

(3,54)*(4,33) ≈ 15,32

On the right side:
(x/20)^0,25 = √x/20
(3x/80)^0,75 = √√3x/80

(√x/20) (√√3x/80)
= (√x (√√3x))/(20 80^(1/4))
= (√x √(√(3x)))/(20 * 2√10)
= (√(√x(√(3x))))/(40√10)
= (x)^(5/8) / (40√10)

Now, we set these equal to each other:
15,32 = (x)^(5/8) / (40√10)

To solve for x, we first multiply both sides by 40√10:
15,32 * 40√10 = x^(5/8)
612,8√10 = x^(5/8)

Now, raise both sides to the power of 8/5 to solve for x:
(x^(5/8))^(8/5) = (612,8√10)^(8/5)
x = (612,8√10)^(8/5)

Therefore, the value of x is approximately equal to (612,8√10)^(8/5).