What is ln(1/(1-e^{-a/x)}) ?

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

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simplify ln(1/(1-e^{-a/x)})

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (- e^{- \frac{a}{x}} + 1)

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

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

ln (\frac{x ^{2} ( 3 - x ) ^{\frac{2}{3}}}{x ^{2} + x + 1})

π (512 (ln (\frac{7}{2}) - ln (\frac{3}{2})) - \frac{5993}{15})

5 lo g_{7} (a) - 2 lo g_{7}^{b} (x)

ln (1.6 \cdot π)

3 lo g_{e} (2) + 5 lo g_{e} (π) - lo g_{e} (9)

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