Final answer:
The positive solution to the equation 8x^(8/7)+27=524315 is x = 16384. This was found by isolating the term with the variable, simplifying the right side by recognizing it as a power of 2, and then applying root operations.
Step-by-step explanation:
The question is asking to find the positive solution to the equation 8x(8/7)+27=524315. First, subtract 27 from both sides to isolate the term with the variable: 8x(8/7) = 524288. Recognizing that 524288 is 219 and that it is divisible by 8, we can then divide both sides by 8, giving x(8/7) = 219 / 8 = 216.
Next, we find the 7th root of both sides to get x8 = 216 / 7 = 2(16*7/8). Now we find the square root of both sides to finally obtain x = 214, which is 16384 as the positive solution.