For which logarithmic expression does logb(x^k) produce a multiplication of k?

The expression logb(x^k) is evaluated using the logarithmic property that states logb(a^c) = c * logb(a). In this case, if you substitute x for a and k for c, it simplifies to logb(x^k) = k * logb(x). This shows that when you take the logarithm of x raised to the power of k, the exponent k comes out in front as a multiplication factor.

This property is fundamental in manipulating logarithmic expressions and is consistent across logarithmic bases. Therefore, option B is indeed the expression for which logb(x^k) produces a multiplication of k.

The other options reflect different operations that do not yield this particular multiplication effect. For example, logarithmic expressions involving division or addition, like those in the other choices, utilize different logarithmic properties that do not allow for an exponent to be factored out in the same manner. Hence, B stands out as the only option where the multiplication of k occurs directly from the logarithmic property being applied.