\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The random variable \(X\) has the density \( f(x) = \frac{1}{\ln(2) x} \), on the interval \([1, 2]\). Calculate \(E(X)\).\FieldText{1}{$$\begin{aligned}[t] E(X) &= \int_{1}^{2} x \frac{1}{\ln(2) x} \, dx \\ &= \frac{1}{\ln 2} \int_{1}^{2} 1 \, dx \\ &= \frac{1}{\ln 2} \left[ x \right]_{1}^{2} \\ &= \frac{1}{\ln 2} (2 - 1) \\ &= \frac{1}{\ln 2} \end{aligned}$$}