Final answer:
The transformation of the function y = log x would result in y = log (xn) which can be rewritten as: y = n · log x.
Step-by-step explanation:
To write an equation for the transformation of the function y = log x, one must apply the rules of logarithms.
The properties of logarithms that are often used in transformation include:
- The property that the logarithm of a number raised to an exponent equals the product of the exponent and the logarithm of the number.
- The property that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.
- The fact that the exponential and natural logarithm functions are inverses of each other, meaning ln (ex) = x and eln x = x.
If we apply an exponent to x, for instance, the transformation would result in y = log (xn) which can be rewritten as:
y = n · log x { using the first property mentioned.
Similarly, if the transformation involves division, we would use the second property.
These transformations reflect how manipulating the input of the logarithm function (x) affects the output (y).