What is ln(e^3+e^{-3})-ln(2) ?

The solution to ln(e^3+e^{-3})-ln(2) is ln((e^6+1)/(2e^3))

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simplify ln(e^3+e^{-3})-ln(2)

simplify

ln (e^{3} + e^{- 3}) - ln (2)

ln (\frac{e ^{6} + 1}{2 e ^{3}})

Decimal Notation

2.30932 \dots

Solution steps

ln (e^{3} + e^{- 3}) - ln (2)

Apply log rule:

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

ln (e^{3} + e^{- 3}) - ln (2) = ln (\frac{e ^{- 3} + e ^{3}}{2})

= ln (\frac{e ^{3} + e ^{- 3}}{2})

\frac{e ^{3} + e ^{- 3}}{2} = \frac{e ^{6} + 1}{2 e ^{3}}

= ln (\frac{e ^{6} + 1}{2 e ^{3}})

ln (\frac{100}{65})

2 + 2 ln (5 x)

ln^{2} (3 e) - 3 ln (3) - 3

ln (P) + 2 ln (1 + x)

ln (A \cdot B)

What is ln(e^3+e^{-3})-ln(2) ?
The solution to ln(e^3+e^{-3})-ln(2) is ln((e^6+1)/(2e^3))