What is ln(2-sqrt(5))-ln(e^2+sqrt(e^4+1)) ?

The solution to ln(2-sqrt(5))-ln(e^2+sqrt(e^4+1)) is ln(-(2-sqrt(5))(e^2-sqrt(e^4+1)))

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simplify ln(2-sqrt(5))-ln(e^2+sqrt(e^4+1))

simplify

ln (2 - 5) - ln (e^{2} + e^{4} + 1)

ln (- (2 - 5) (e^{2} - e^{4} + 1))

Solution steps

ln (2 - 5) - ln (e^{2} + e^{4} + 1)

Apply log rule:

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

ln (2 - 5) - ln (e^{2} + e^{4} + 1) = ln (\frac{2 - 5}{e ^{2} + e ^{4} + 1})

= ln (\frac{2 - 5}{e ^{2} + e ^{4} + 1})

\frac{2 - 5}{e ^{2} + e ^{4} + 1} = - (2 - 5) (e^{2} - e^{4} + 1)

= ln (- (2 - 5) (e^{2} - e^{4} + 1))

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

ln ∣ x ∣ - ln x^{2}

- 1423.586575 \cdot lo g_{10} (\frac{0.1}{1})

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

lo g_{10} (\frac{\frac{1}{256}}{\frac{125}{4}})

What is ln(2-sqrt(5))-ln(e^2+sqrt(e^4+1)) ?
The solution to ln(2-sqrt(5))-ln(e^2+sqrt(e^4+1)) is ln(-(2-sqrt(5))(e^2-sqrt(e^4+1)))