What is expand ln((4x)/((1-y))) ?

The solution to expand ln((4x)/((1-y))) is 2ln(2)+ln(x)-ln(1-y)

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expand ln((4x)/((1-y)))

expand

ln (\frac{4 x}{( 1 - y )})

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

Solution steps

ln (\frac{4 x}{( 1 - y )})

Apply log rule:

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

ln (\frac{4 x}{( 1 - y )}) = ln (4 x) - ln ((1 - y))

= ln (4 x) - ln (- y + 1)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (4 x) = ln (4) + ln (x)

= ln (4) + ln (x) - ln (- y + 1)

ln (4) = 2 ln (2)

= 2 ln (2) + ln (x) - ln (- y + 1)

ln (\frac{x - 8}{x + 2})

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

50 ln (\frac{143.33}{50}) + 14

0.5 [ln (1 - 0.68) - ln (1 + 0.68)]

ln (b \cdot e^{- c \cdot x})

What is expand ln((4x)/((1-y))) ?
The solution to expand ln((4x)/((1-y))) is 2ln(2)+ln(x)-ln(1-y)