Final answer:
When multiplying logs with a different base, none of the provided options A, B, C directly apply. Instead, if the logs involve exponents, you use the power rule, which means multiplying the exponent by the log of the base. This corresponds to option D, which involves taking the logarithm of the result.
Step-by-step explanation:
The question asks about operations with logarithms, specifically how to multiply logarithms with a different base. To clarify, you cannot directly multiply two logarithms together and get another logarithm as a result. However, you can use properties of logarithms to work with multiples and exponents.
When dealing with multiplying numbers inside a logarithm (same base), you use the product rule for logarithms: log(xy) = log(x) + log(y). This property allows you to turn the multiplication of numbers inside a log into an addition of two logs.
On the other hand, when you raise a number to an exponent and then take the logarithm, you use the power rule: log(x^y) = y*log(x). The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number itself.
For dividing two numbers inside a log, you would use the quotient rule: log(x/y) = log(x) - log(y). This results in the subtraction of one log from another.
Answer
In the context of the provided options, none directly address the concept of multiplying logs with different bases. However, if we interpret the question as asking about the log of an exponent (option A), then the relevant rule would be the power rule, meaning the correct operation when an exponent is involved in a logarithm is to multiply the exponent by the logarithm of the base (option D: You take the logarithm of the result).