Final answer:
To solve the equation, we rewrite the bases to be the same and then set the exponents equal to each other. After simplification, the equation becomes (1/2) + X = 5/2, giving us a solution of X = 2.
Step-by-step explanation:
To solve the equation 81/6 x 2X = 321/2, let's first simplify each side.
The base 8 is equal to 23, and thus 81/6 can be rewritten as
(23)1/6 = 23/6 = 21/2.
Similarly, 32 is equal to 25, so 321/2 can be written as
(25)1/2 = 25/2.
Our equation now becomes
21/2 x 2X = 25/2.
Using the property of exponents that am x an = am+n, we can combine the exponents on the left side to get
2(1/2)+X = 25/2.
This gives us the equation
(1/2) + X = 5/2.
Solving for X, we subtract 1/2 from both sides and find that
X = 5/2 - 1/2 = 4/2 = 2.
Therefore, the value of X is 2.