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Popular >

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

Solution

simplify

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

Solution

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

+1

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

2 ln (e) = 2

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

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Frequently Asked Questions (FAQ)

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