**Solution:**

To find the value of x/y, we first need to solve the given equations for x and y.

**Equation 1: 3^x - 1 = 9**

To solve this equation, we can rewrite it as:

3^x = 9 + 1

3^x = 10

Taking the logarithm of both sides, we have:

log(3^x) = log(10)

Using the property of logarithms, we can bring down the exponent:

x * log(3) = log(10)

Now, we can solve for x by dividing both sides by log(3):

x = log(10) / log(3)

**Equation 2: 4^(y^2) = 64**

To solve this equation, we can rewrite it as:

4^(y^2) = 4^3

Since the bases are equal, we can equate the exponents:

y^2 = 3

Taking the square root of both sides, we have:

y = √3

Now, we can substitute the values of x and y into the expression x/y to find the value:

x/y = (log(10) / log(3)) / √3

Simplifying the expression, we can rationalize the denominator by multiplying the numerator and denominator by √3:

x/y = (log(10) / log(3)) * (√3 / √3)

x/y = (log(10) * √3) / (log(3) * √3)

Since log(10) is equal to 1, we have:

x/y = (√3) / (log(3) * √3)

The square root terms cancel out, leaving us with:

x/y = 1 / log(3)

Therefore, the value of x/y is 1 / log(3).