Question

Simplify the given logarithmic expressions:

A. 6−log 9


B. a+2−log b


C. u−3−log 12


D. log 15 +log2 4−log 26

Answer 1

Only expression D can be partially simplified using logarithm properties to log(15/26). The other expressions, A, B, and C, cannot be simplified further without additional context or information.

Step-by-step explanation:

To simplify the given logarithmic expressions, we follow the properties of logarithms. Unfortunately, expressions A, B, and C do not contain any operable logarithmic properties as they are not interacting with other logarithmic terms directly. However, expression D can be simplified using the properties of logarithms which state that the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers.

1. For expression A: 6−log 9, it cannot be simplified further without additional context.
2. Similarly, for expression B: a+2−log b, this expression cannot be simplified further without additional context.
3. For expression C: u−3−log 12, this too cannot be simplified further without additional context.
4. Finally, for expression D: log 15 + log2 4−log 26, we note that log2 4 is an independent term since it is a log base 2, not base 10 like the others. Thus we can only combine the base 10 logs: log 15 − log 26. This results in log(15/26), but the log2 4 term remains separate.