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

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

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simplify ln((-1+e^2)/(2e))

simplify

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

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

Decimal Notation

0.16143 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 e) = ln (2) + ln (e)

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

Apply log rule:

lo g_{a} (a) = 1

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

- (ln (2) + 1) : - ln (2) - 1

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

lo g_{x} (5) + lo g_{x} (5 x) - 2.25

ln (2 (3))

lo g_{a} (\frac{x ^{2} y ^{3}}{z ^{4}})

lo g_{6} (a b^{3} c^{2})

lo g_{10} (\frac{x}{y}) + lo g_{10} (\frac{y ^{2}}{x})

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