Final answer:
The equation log(9)(11+3x)=6 can be rewritten in its exponential form to solve for x, leading to the solution x = 531430/3. Option d seems to be the closest to the correct answer, though it appears to be a typo in the provided options.
Step-by-step explanation:
To solve the logarithmic equation log(9)(11+3x)=6, we need to use the properties of logarithms to isolate the variable x. First, we will convert the logarithmic equation into its equivalent exponential form using the fact that if logb(a) = c, then bc = a. Therefore, we have:
96 = 11 + 3x
Doing the math:
- 96 = 531441
- 531441 = 11 + 3x
- 531441 - 11 = 3x
- 531430 = 3x
- x = 531430 / 3
- x = 177143.333...
So the solution for x in terms of a whole number and fractional part is 531430/3, which is not one of the provided options. The closest option is d. 531430/3 if we assume that the last two digits of the numerator are a typo in the answer choices. Assuming there was a misprint, the correct choice would be d. 531430/3.