What is ln(b/(1-b))-ln(a/(1-a)) ?

The solution to ln(b/(1-b))-ln(a/(1-a)) is ln((b(1-a))/(a(1-b)))

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simplify ln(b/(1-b))-ln(a/(1-a))

simplify

ln (\frac{b}{1 - b}) - ln (\frac{a}{1 - a})

ln (\frac{b ( 1 - a )}{a ( 1 - b )})

Solution steps

ln (\frac{b}{1 - b}) - ln (\frac{a}{1 - a})

Apply log rule:

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

ln (\frac{b}{1 - b}) - ln (\frac{a}{1 - a}) = ln (\frac{\frac{b}{- b + 1}}{\frac{a}{- a + 1}})

= ln (\frac{\frac{b}{1 - b}}{\frac{a}{1 - a}})

Divide fractions:

\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a \cdot d}{b \cdot c}

= ln (\frac{b ( 1 - a )}{a ( 1 - b )})

- 0.375 lo g_{2} (0.375) - 0.625 lo g_{2} (0.625)

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

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

- lo g_{10} (9.6 \cdot 1 0^{- 3})

- 8 + \frac{52 \cdot ln ( 2 )}{3}

What is ln(b/(1-b))-ln(a/(1-a)) ?
The solution to ln(b/(1-b))-ln(a/(1-a)) is ln((b(1-a))/(a(1-b)))