**Solution:**

To find the value of log₁₉ 3, we need to express 3 as a power of 9.

Let's start by expressing 3 as a power of 9.

3 = 9^(1/2)

Now we can rewrite the expression log₁₉ 3 as log₁₉ (9^(1/2)).

Using the logarithmic property logₐ (x^y) = y * logₐ (x), we can simplify the expression further.

log₁₉ (9^(1/2)) = (1/2) * log₁₉ 9

Now we need to find the value of log₁₉ 9.

To do this, we need to express 9 as a power of 19.

9 = 19^(2/2)

Now we can rewrite the expression as (1/2) * log₁₉ (19^(2/2)).

Using the logarithmic property logₐ (x^y) = y * logₐ (x), we can simplify the expression further.

(1/2) * log₁₉ (19^(2/2)) = (1/2) * (2/2) * log₁₉ 19

Simplifying the expression, we get:

(1/2) * (2/2) * log₁₉ 19 = (1/2) * log₁₉ 19

Therefore, the value of log₁₉ 3 is (1/2) * log₁₉ 19.

Since the question asks for the value of log₁₉ 3 to the base 9, we need to convert the expression to base 9.

Using the change of base formula, we can rewrite the expression as:

log₁₉ 3 = (log 3) / (log 19)

So, the value of log₁₉ 3 is (log 3) / (log 19).

Since none of the given options match this value, the correct answer is (d) none of these.

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