5. (1 point) Which of the following is the change of base formula? a. $\log _{a} x=\log _{x} a$ b. $\log _{a} x=(\log x)(\log a)$ c. $\log _{a} x=\frac{\log a}{\log x}$ d. $\log _{a} x=\frac{\log x}{\log a}$ e. none of these 5.

Step 1 ：The change of base formula is a mathematical formula used to change the base of a logarithm. The formula is as follows: \(\log _{a} x=\frac{\log b x}{\log b a}\) where a, b, and x are positive real numbers and a ≠ 1, b ≠ 1. This formula allows us to compute the logarithm of a number in one base in terms of the logarithm of that number in another base.

Step 2 ：Looking at the options given in the question, the correct formula is represented by option d.

Step 3 ：Final Answer: \(\boxed{\text{d. } \log _{a} x=\frac{\log x}{\log a}}\)