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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Simplify

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

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

ln (x e)

lo g_{d} (x^{4})

lo g_{10} (\frac{x y}{ab})

6 [ln (z) + ln (z + 8)] - 3 ln (z - 8)

ln (y x)

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