What is e^{-log_{e}(((x-1))/x)} ?

The solution to e^{-log_{e}(((x-1))/x)} is x/(x-1)

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simplify e^{-log_{e}(((x-1))/x)}

simplify

e^{- l o g_{e} (\frac{( x - 1 )}{x})}

\frac{x}{x - 1}

Solution steps

e^{- l o g_{e} (\frac{( x - 1 )}{x})}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{l o g_{e} (\frac{x - 1}{x})}}

e^{l o g_{e} (\frac{x - 1}{x})} = \frac{x - 1}{x}

= \frac{1}{\frac{x - 1}{x}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{x}{x - 1}

- e^{- x} \cdot e^{x} \cdot e^{2 x}

e^{- 1}

25.637 \cdot 1 0^{- 2} \cdot 81.25

e^{- s \cdot t}

e^{- 16} e^{7}

What is e^{-log_{e}(((x-1))/x)} ?
The solution to e^{-log_{e}(((x-1))/x)} is x/(x-1)