2(LOG 2 X)+3=0

Solve for X:
3 + (2 log(X))/(log(2)) = 0

Bring 3 + (2 log(X))/(log(2)) together using the common denominator log(2):
(3 log(2) + 2 log(X))/(log(2)) = 0

Multiply both sides by log(2):
3 log(2) + 2 log(X) = 0

Subtract 3 log(2) from both sides:
2 log(X) = -3 log(2)

Divide both sides by 2:
log(X) = -(3 log(2))/2

-(3 log(2))/2 = log(1/2^(3/2)) = log(1/(2 sqrt(2))):
log(X) = log(1/(2 sqrt(2)))

Cancel logarithms by taking exp of both sides:
Answer: |X = 1/(2 sqrt(2))

2(LOG₂X)+3=0    subtract 3 from each side

2(LOG₂X)   = -3     divide both sides by 2

(LOG₂X)  = -3/2     In exponential terms, we have that

2^-3/2  =  x         means the same as

(1/2) ^3/2   = x    ....so....

x = [(1/2)^3] ^(1/2)   =    √(1/8)    =   (1/2)(1/√2)  =   1 / [2√2]