If the base of the log in the RHS is 10, then 

Solution:

Given, log2 (9 - 2X) = 10log (3-x)

Using the logarithmic identity, logb (x^a) = alogb (x), we can write the equation as:

log2 [(9 - 2X)/(3 - x)^10] = 0

Taking antilogarithm (base 2) on both sides, we get:

[(9 - 2X)/(3 - x)^10] = 2^0

Simplifying, we get:

9 - 2X = 3 - x^10

2X - x^10 = 6

Now, we need to solve for x.

Let's check the options one by one.

Option (d) - 0 and 6:

If x = 0, then 9 - 2X = 9 and 3 - x = 3. Substituting these values in the given equation, we get:

log2 9 = 10log 3

This equation is not true, hence x = 0 is not a solution.

If x = 6, then 9 - 2X = -3 and 3 - x = -3. Substituting these values in the given equation, we get:

log2 (-3) = 10log (-3)

This equation is not defined, hence x = 6 is not a solution.

Therefore, option (d) is not the correct answer.

Option (b) - 3:

If x = 3, then 9 - 2X = 3 and 3 - x = 0. Substituting these values in the given equation, we get:

log2 3 = 10log 0

The right-hand side of this equation is not defined, hence x = 3 is not a solution.

Therefore, option (b) is not the correct answer.

Option (a) - 0:

If x = 0, then 9 - 2X = 9 and 3 - x = 3. Substituting these values in the given equation, we get:

log2 9 = 10log 3

This equation is true, hence x = 0 is a solution.

Therefore, the correct answer is option (a) - 0.