What is ln((e^{2x})/(e^{2x)+1}) ?

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

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simplify ln((e^{2x})/(e^{2x)+1})

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 x ln (e) = 2 x

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

ln (4 e^{- \frac{6}{100} t})

20 e^{9} + ln (12) + 50 - ln (9)

- lo g_{10} (2.3 \cdot 1 0^{- 9})

ln (\frac{1}{2 ^{n}} \cdot e^{- 2 x} e^{- 3 t})

\frac{3}{2} (lo g_{10} (4.94145) - lo g_{10} (761.21))

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