Final answer:
The statement 'a) log₅ 125 = 3' is equivalent to 5³ = 125 because it accurately represents the exponentiation relationship using logarithms, where the base 5 raised to the power 3 results in 125. The other options misrepresent the relationship between base, exponent, and result.
Step-by-step explanation:
The question asks which statement is equivalent to 5³ = 125. This can be connected to logarithms since logarithms are the inverse operations to exponentiation. Statement 'a) log₅ 125 = 3' is equivalent because the base of the logarithm (5) raised to the result (3) equals 125, which is the original statement's claim. Knowing that the logarithm of a number is the exponent to which the base must be raised to get that number explains why the other options are incorrect:
- 'b) log₁₂₅ 5 = 3' incorrectly suggests that 125 raised to some power equals 5.
- 'c) log₃ 5 = 125' incorrectly implies that 3 raised to the power of 125 equals 5.
- 'd) log₅ 3 = 125' incorrectly claims that 5 raised to the power of 125 equals 3.
Therefore, the original exponentiation can be expressed as its logarithmic equivalent in statement a), which correctly uses the logarithm properties.