Log Question Solution

I asked gpt and this is what it told me. I also find this very reasonable.

Step 6: Why the solution does not depend on a

Notice that the process of simplifying the equation to a quadratic form (i.e., ) completely removes the logarithmic terms involving . The only place where was involved was in the logarithmic expressions but because these terms cancel out (as long as ), the resulting quadratic equation no longer depends on a.

Thus, the equation simplifies to a quadratic equation in that only has the coefficients 4, -5, and -6, which do not depend on . Therefore, the solution for is completely independent of , and it holds true for any positive value of .

Conclusion:

The number of distinct values of is determined solely by the solutions to the quadratic equation , which has two distinct solutions: and . The value of does not affect this outcome because it cancels out during the simplification process.

Hence, the answer is 2 distinct values of x and the equation does not depend on the value of a.