Final answer:
The value of log (b⁸ / (³√a⁸c⁸)) using the given logarithmic values does not match any of the provided options. A detailed step-by-step calculation suggests an error in the evaluation or given information since the result we find is -120.
Step-by-step explanation:
The given logarithmic values are log a = 15, log b = -5, and log c = 15. The expression to evaluate is log (b⁸ / (³√a⁸c⁸)). Using the properties of logarithms, we can simplify the expression:
log (b⁸) - log (³√a⁸c⁸)
8 · log (b) - log ((a⁸c⁸)¹)
8 · (-5) - (1/3) · log (a⁸c⁸)
8 · (-5) - (1/3) · (log (a⁸) + log (c⁸))
8 · (-5) - (1/3) · (8 · log (a) + 8 · log (c))
-40 - (1/3) · (8 · 15 + 8 · 15)
-40 - (1/3) · (120 + 120)
-40 - (1/3) · 240
-40 - 80
-120
However, the calculation above does not match any of the given answer choices. It appears there may have been an error in the calculation or in the interpretation of the initial expression or given choices. Please recheck for any possible missteps or additional context that might change the evaluation.