Final answer:
The equation 2⁻³=1/8 can be expressed in logarithmic form as log2(1/8) = -3. This uses the principle that logarithmic functions are the inverses of exponential functions.
Step-by-step explanation:
To express the equation 2⁻³=1/8 in logarithmic form, we start by recalling that the equation a⁻⁴=b can be rewritten as loga(b)=-c. In this case, our base (a) is 2, our exponent (c) is -3, and b is 1/8. Therefore, the logarithmic form of the equation is log2(1/8) = -3.
The mathematical properties we used for the conversion include understanding that exponential and logarithmic functions are inverses of each other. This principle is a foundational concept in algebra and is key in manipulating equations from exponential to logarithmic form and vice versa.