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Example 28 - Is it true that x= elog x for all real x? - Examples

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Example 28 Is it true that x= 𝑒 log﷮𝑥﷯ for all real x? x = e log x For x = 0 0 = elog 0 But log 0 is not defined. Hence, the equation is not defined for x = 0 For x < 0 x = e log x But log x is not defined for negative numbers Hence equation is not defined for x < 0 For x > 0 x = e log x This is defined Hence, equation is defined for x > 0 Therefore, x = e log x is true for all positive values if x i.e. x > 0

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