Final answer:
The correct expression using the properties of logarithms is 'log(s) + log(s^B) + log(t^-3)', combining the individual logarithms into a single logarithm of the combined terms.
Step-by-step explanation:
The expression given is log(s) + B log(s) - 3 log(t), and we can use the properties of logarithms to simplify this to a single logarithm. According to the property that the logarithm of a number raised to an exponent (log(a^x) = x log(a)), we can rewrite B log(s) as log(s^B), and similarly, -3 log(t) as log(t^-3). Additionally, the property that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log(xy) = log(x) + log(y)), and the logarithm of the number resulting from the division of two numbers is the difference between the logarithms of the two numbers (log(x/y) = log(x) - log(y)), we can combine the terms into a single logarithm.
Combining these properties, the expression becomes log(s) + log(s^B) - log(t^3), which can be written as log(s × s^B / t^3). Therefore, the correct option is b. log(s) + log(s^B) + log(t^-3), since log(t^-3) is equivalent to -log(t^3).