**Solution:**

To find the value of log^10 60, we can use the properties of logarithms to express 60 as a product or quotient of numbers whose logarithms we already know.

**Step 1: Express 60 as a product of prime numbers**
To find the prime factorization of 60, we can divide it by prime numbers until we obtain only prime factors. We have:

60 ÷ 2 = 30
30 ÷ 2 = 15
15 ÷ 3 = 5

Therefore, the prime factorization of 60 is 2 × 2 × 3 × 5.

**Step 2: Express 60 as a product of numbers whose logarithms we know**
Using the prime factorization of 60, we can rewrite it as:

60 = 2 × 2 × 3 × 5

Now, we can use the property of logarithms that states log a (mn) = log a (m) + log a (n) to express 60 as a sum of logarithms. We have:

log^10 60 = log^10 (2 × 2 × 3 × 5)

Using the property mentioned above, we can rewrite this as:

log^10 60 = log^10 2 + log^10 2 + log^10 3 + log^10 5

**Step 3: Substitute the given values of x and y**
Given that log^10 2 = x and log^10 3 = y, we can substitute these values into the expression above to get:

log^10 60 = x + x + y + log^10 5

**Step 4: Simplify the expression**
We can further simplify the expression by adding the values of x and y:

log^10 60 = 2x + y + log^10 5

Therefore, the value of log^10 60 is expressed as 2x + y + log^10 5.