Given:
(110)x = (132)4

To find:
The value of x

Solution:

Step 1: Convert the given numbers from base 4 to base 10.

(110)x = (132)4

Converting (132)4 to base 10:
(132)4 = (1 × 4^2) + (3 × 4^1) + (2 × 4^0)
= (1 × 16) + (3 × 4) + (2 × 1)
= 16 + 12 + 2
= 30

Step 2: Convert (110)x to base 10.

To convert (110)x to base 10, we need to know the value of x. Let's assume x = n.

(110)n = (1 × n^2) + (1 × n^1) + (0 × n^0)
= (n^2) + n

Step 3: Equate the values obtained in step 1 and step 2.

(n^2) + n = 30

Step 4: Solve the equation to find the value of x.

(n^2) + n - 30 = 0

This is a quadratic equation. To solve it, we can factorize it or use the quadratic formula.

Factoring the equation, we get:
(n - 5)(n + 6) = 0

Setting each factor equal to zero, we have:
n - 5 = 0 or n + 6 = 0

Solving for n, we get:
n = 5 or n = -6

Since n represents the base, it cannot be negative. Therefore, n = 5.

Step 5: Substitute the value of x back into the original equation.

Substituting x = 5 into (110)x:
(110)5 = (1 × 5^2) + (1 × 5^1) + (0 × 5^0)
= (25) + (5) + (0)
= 30

Therefore, x = 5 is the correct answer.

Answer:
The value of x is 5.