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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

ln ((2 x + 1) (x - 4))

ln (2 cos (\frac{x}{2}))

ln (3 - 2 x) - 2 ln (x)

ln (\frac{2}{72})

f (b) = ln (4 b)

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