Final answer:
To write an expression as a sum and/or difference of logarithms with powers expressed as factors, apply the properties of logarithms. The product rule states that log(xy) is the sum of log(x) and log(y), and powers within a logarithm can be brought out as a factor: log(x^a) = a log(x). A calculator can aid in confirming these properties through functions like LOG and ln.
Step-by-step explanation:
The process of writing an expression as a sum and/or difference of logarithms and expressing powers as factors is an application of the logarithmic properties.
For instance, the logarithm of a product of two numbers is expressed as the sum of the logarithms of the individual numbers.
This can be shown as log xy = log x + log y, and for natural logarithms, ln xy = ln x + ln y. Similarly, when dealing with exponents, powers within a logarithm can be brought out as a factor, for example, log(x^a) = a log(x).
To perform these operations without a calculator, one must understand and apply the properties of logarithms. When working with a calculator, the LOG and ln buttons can be used to find the common and natural logarithms, respectively. For subprocesses, such as squaring or taking roots, as well as exponential functions and their inverses, calculators can help in validating the rules of logarithms through experimentation.