Final answer:
The change of base formula allows us to convert log₇(1/3) to a more convenient base for calculation; the correct formula is log₇(1/3) = log₁₀(1/3)/log₁₀(7) or log₇(1/3) = ln(1/3)/ln(7). Option C is correct.
Step-by-step explanation:
The change of base formula is used to rewrite logarithms in terms of a base that is more convenient, usually to allow for easier calculation using a calculator. In the context of the given problem, we want to convert log₇(1/3) to a base that our calculator can handle, typically base 10 or the natural logarithm base, e.
The correct application of the change of base formula is given by:
log₇(1/3) = log₁₀(1/3)/log₁₀(7) or log₇(1/3) = ln(1/3)/ln(7)
This is because the change of base formula states that for any logarithm of the form logₓ(b), it can be expressed as logₓ(b) = logₙ(b)/logₙ(a), where x is any positive base you choose for your calculations, and typically one that your calculator supports (x=10 or e for the common logarithm or natural logarithm, respectively).