What is the logarithmic function formula derived from the exponential equation a^x = y?

What is the logarithmic function formula derived from the exponential equation a^x = y?

• A. log a y = x
• B. y = a^log a x
• C. log y = ax
• D. y = log a x

Answer: (A)

The logarithmic function formula derived from the exponential equation \(a^x = y\) is represented by the relationship where the logarithm is the inverse of exponentiation. Specifically, if you have an equation in the form \(a^x = y\), taking the base \(a\) logarithm of both sides allows you to solve for \(x\). This relationship can be expressed as follows: to find \(x\) in terms of \(y\), we can rewrite the original equation as \(x = \log_a y\). When rearranged, this gives the logarithmic function formula \( \log_a y = x\). Thus, it shows how to express the exponent in terms of the base and the output \(y\). This indicates that the logarithm answers the question: "To what exponent must the base \(a\) be raised in order to produce \(y\)?" The other options present different equations or forms that do not accurately represent the inverse relationship between logarithms and exponentials as derived from the original equation.

The logarithmic function formula derived from the exponential equation (a^x = y) is represented by the relationship where the logarithm is the inverse of exponentiation. Specifically, if you have an equation in the form (a^x = y), taking the base (a) logarithm of both sides allows you to solve for (x).

This relationship can be expressed as follows: to find (x) in terms of (y), we can rewrite the original equation as (x = \log_a y). When rearranged, this gives the logarithmic function formula ( \log_a y = x). Thus, it shows how to express the exponent in terms of the base and the output (y).

This indicates that the logarithm answers the question: "To what exponent must the base (a) be raised in order to produce (y)?" The other options present different equations or forms that do not accurately represent the inverse relationship between logarithms and exponentials as derived from the original equation.