What is ln(2/(|e^{(-1))+e|}) ?

The solution to ln(2/(|e^{(-1))+e|}) is ln(2)-ln(1/e+e)

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simplify ln(2/(|e^{(-1))+e|})

simplify

ln (\frac{2}{e ^{(- 1)} + e})

ln (2) - ln (\frac{1}{e} + e)

Decimal Notation

- 0.43378 \dots

Solution steps

ln (\frac{2}{e ^{(- 1)} + e})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{2}{e ^{(- 1)} + e}) = ln (2) - ln e^{(- 1)} + e

= ln (2) - ln e^{- 1} + e

ln e^{- 1} + e = ln (\frac{1}{e} + e)

= ln (2) - ln (e + \frac{1}{e})

\frac{1}{2} ln (\frac{π}{4}) + c

ln (\frac{2 ^{- 1}}{3 ^{2} \cdot 5 ^{1}})

ln (9) + 2 ln (4) - ln (2)

\frac{ln ( 29500 ) - ln ( 100 )}{ln ( 75000 ) - ln ( 100 )}

ln (\frac{1.5}{11})

What is ln(2/(|e^{(-1))+e|}) ?
The solution to ln(2/(|e^{(-1))+e|}) is ln(2)-ln(1/e+e)