What is ln(sqrt(e^x+1)-1)-ln(sqrt(1+e^x)+1) ?

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

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simplify ln(sqrt(e^x+1)-1)-ln(sqrt(1+e^x)+1)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

ln (\frac{1}{x 2 π})

ln (41 x^{- 4} y)

\frac{ln ( 3939.6896 ) - ln ( 1992.1294 )}{3416.708}

ln (4^{3} + 4) - ln (8 \cdot (4)^{3} + 15 (4))

ln (\frac{327.15}{243.15})

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