Final Answer:
The logarithmic form of 5⁻² = 1/25 is log₅(1/25) = -2.
Step-by-step explanation:
In logarithmic form, the expression 5⁻² = 1/25 can be represented as log₅(1/25) = -2. To understand this transformation, let's break it down step by step.
In the given exponential expression, 5⁻², the base is 5, and the exponent is -2. This is equivalent to saying 1/5², as a negative exponent indicates the reciprocal. Therefore, 5⁻² is the same as 1/25.
Now, in logarithmic form, log₅(1/25) = -2. Here, the base of the logarithm is 5, the result is -2, and the argument of the logarithm is 1/25. The logarithmic expression essentially tells us that 5 raised to the power of -2 equals 1/25. Logarithms are a useful tool for expressing exponential relationships in a different form, making it easier to work with certain mathematical problems. In this case, the logarithmic form provides a concise way to represent the relationship between the base 5 and the result 1/25.