Start from the very basic definition!

Algebra Level 3

$\large { e }^{ -\sqrt { \left| \ln\{ x\} \right| } }-{ \{ x\} }^{ 1/\sqrt { \left| \ln\{ x\} \right| } }$

Evaluate the expression above for $x\ne 0$

Notation : $\{ \cdot \}$ denotes the fractional part function .

The answer is 0.

1 solution

Chew-Seong Cheong
Aug 22, 2017

$\large \begin{aligned} X & = e^{-\sqrt{|\ln \{x\}|}} - \{x\}^{\frac 1{\sqrt{|\ln \{x\}|}}} \\ & = e^{-\sqrt{|\ln \{x\}|}} - e^{\frac {\ln \{x\}}{\sqrt{|\ln \{x\}|}}} \\ & = e^{-\sqrt{|\ln \{x\}|}} - e^{\frac {-|\ln \{x\}|}{\sqrt{|\ln \{x\}|}}} \\ & = e^{-\sqrt{|\ln \{x\}|}} - e^{-\sqrt{|\ln \{x\}|}} \\ & = \boxed{0} \end{aligned}$

Start from the very basic definition!

The answer is 0.

1 solution

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