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

The solution to ln(e^2-e^{-2})-ln(e-e^{-1}) is ln((e^4-1)/(e^3-e))

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

simplify

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

ln (\frac{e ^{4} - 1}{e ^{3} - e})

Decimal Notation

1.12692 \dots

Solution steps

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

Apply log rule:

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

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

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

\frac{e ^{2} - e ^{- 2}}{e - e ^{- 1}} = \frac{e ^{4} - 1}{e ^{3} - e}

= ln (\frac{e ^{4} - 1}{e ^{3} - e})

ln ∣ x - 1 ∣ - ln ∣ x + 4 ∣

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

\frac{1}{4} ln (\frac{2 - 1}{2 + 1})

4 lo g_{10} (x - 6) - 5 lo g_{10} (x)

3 (lo g_{2} (x) - 4 lo g_{2} (y)) + 2 lo g_{2} (w)

What is ln(e^2-e^{-2})-ln(e-e^{-1}) ?
The solution to ln(e^2-e^{-2})-ln(e-e^{-1}) is ln((e^4-1)/(e^3-e))