Question Detail

To find the derivative of a logarithm with an arbitrary base, we first convert it to the natural logarithm using the change of base formula: logb x = ln x / ln b.In this case, y = log2 x = ln x / ln 2.Now, differentiate with respect to x:dy/dx = d/dx [ln x / ln 2] = (1/ln 2) * d/dx [ln x] = (1/ln 2) * (1/x) = 1/(x ln 2).Comparing this with option B, 1/(x ln a), where a is the base of the logarithm (in this case, a=2), we find a match.