When the tangent to the curve y = x log x is parallel to the chord joining the points (1, 0) and (e, e), the value of x is ______.

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When the tangent to the curve y = x log x is parallel to the chord joining the points (1, 0) and (e, e), the value of x is bb(e^(1/(1−e))). Explanation: Given: y = f\left( x ight) = x\log x Differentiating the given function with respect to x, we get f'\left( x ight) = 1 + \log x \Rightarrow Slope of the tangent to the curve = 1 + \log x Also, Slope of the chord joining the points \left( 1, 0 ight) 	ext { and } \left( e, e ight) (m) = e/e - 1 The tangent to the curve is parallel to the chord joining the points \left( 1, 0 ight) 	ext { and } \left( e, e ight). 	herefore m = 1 + \log x \Rightarrow e/e - 1 = 1 + \log x \Rightarrow e/e - 1 - 1 = \log x \Rightarrow e - e + 1/e - 1 = \log x \Rightarrow 1/e - 1 = \log x \Rightarrow x = e^1/e - 1

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