What is ln((e^4+2e^2)/(1+2e^2)) ?

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

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simplify ln((e^4+2e^2)/(1+2e^2))

simplify

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

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

Decimal Notation

1.48092 \dots

Solution steps

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

Apply log rule:

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

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

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

5 ln (\frac{9}{8}) + 1.5 ln (\frac{13}{9}) + 3 ln (\frac{14}{13})

(ln (c (t)) - ln (c)) e^{r t}

lo g_{e} (x^{4} - 16) - 3 lo g_{e} (x - 2)

ln (5 \cdot 1 0^{12 - 4})

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