Final answer:
Logarithmic differentiation employs the properties of logarithms to differentiate functions that are difficult to handle with standard rules, involving the natural logarithm and exponent rules.
Step-by-step explanation:
The process of logarithmic differentiation is used to find the derivative of functions that can be complex to differentiate directly. To differentiate using this method, first take the natural logarithm of both sides of the equation, using the fact that the natural logarithm and the exponential function are inverses of each other. When dealing with the logarithm of a quotient, we apply the property that says the logarithm of a quotient is the difference of the logarithms. Additionally, when you have a number raised to an exponent, the logarithm of that number is equal to the product of the exponent and the logarithm of the base number.
To evaluate expressions or find the derivative using logarithmic differentiation, substitute known quantities into the equation and then solve. This technique is particularly useful in situations where the function involves exponentials, products or quotients that are not easily differentiated using standard rules. For instance, if you are given the ratio of two intensities, you might need to find the difference in their sound levels in decibels by applying the properties of logarithms.
These properties of logarithms apply regardless of the base, whether you are using the natural logarithm (ln) or base-10 (log). This method provides a more fundamental approach to problems that can otherwise be hard to solve, ensuring a more than 100 words explanation that is clear and accessible.