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).
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).