**Given Information:**
- log 3 base a = 2
- log 8 base b = 3

**To Find:**
- log b base a

**Solution:**

To find log b base a, we need to rewrite the logarithms using the change of base formula.

**Change of Base Formula:**

log a base b = log c base b / log c base a

Using the change of base formula, we can rewrite the given equations as follows:

log 3 base a = log 3 base 10 / log a base 10 = 2

log 8 base b = log 8 base 10 / log b base 10 = 3

Now, let's solve each equation step by step.

**Solving log 3 base a = 2:**

log 3 base 10 / log a base 10 = 2

log 3 base 10 = 2 * log a base 10

log 3 base 10 = log a^2 base 10

3 = a^2

a = √3

**Solving log 8 base b = 3:**

log 8 base 10 / log b base 10 = 3

log 2^3 base 10 / log b base 10 = 3

3 * log 2 base 10 / log b base 10 = 3

log 2 base 10 / log b base 10 = 1

log 2 base b = 1

2 = b

Now, we have found the values of a and b:

a = √3
b = 2

**Finding log b base a:**

log b base a = log 2 base √3

Using the change of base formula:

log 2 base √3 = log 2 base 10 / log √3 base 10

= log 2 base 10 / (1/2) * log 3 base 10

= 2 * log 2 base 10 / log 3 base 10

Now, we know that log 3 base a = 2. Therefore,

2 * log 2 base 10 / log 3 base 10 = 2 * 1 / 2 = 1

So, log b base a is equal to 1.

Therefore, log b base a = 1.