Final answer:
The Power Property of logarithms states that the logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the base number. It can be written as log₂ (Mⁿ) = nlog₂(M) and is a useful property when dealing with logarithms and exponents.
Step-by-step explanation:
The subject of the student's question is logarithms, specifically the Power Property of logarithms. This property states that the logarithm of a number raised to an exponent is equal to the product of that exponent and the logarithm of the number itself. In mathematical terms, this is written as log₂ (Mⁿ) = nlog₂(M). This applies across any base of the logarithm, be it common log or natural ln, with the base often being 10 for common logarithms.
Here is a practical example of this property: let's find the logarithm of 1000. First, recognize that 1000 is equivalent to 10³. Therefore, using the Power Property, we can say that log(1000) is equal to 3 * log(10), which simplifies to 3, because the logarithm of a base (10) to the power of 1 is 0.
In general, this property makes the calculation of logarithms more manageable, especially when dealing with exponents. The ability to convert a logarithm of an exponent into a multiplication problem is particularly useful in solving algebraic equations involving logarithms.