What is expand log_{e}(ysqrt(y/(1-y))) ?

The solution to expand log_{e}(ysqrt(y/(1-y))) is ln(y)+ln(sqrt(y/(1-y)))

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expand log_{e}(ysqrt(y/(1-y)))

expand

lo g_{e} (y \frac{y}{1 - y})

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

Solution steps

lo g_{e} (y \frac{y}{1 - y})

Apply log rule:

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

lo g_{e} (y \frac{y}{1 - y}) = lo g_{e} (y) + lo g_{e} (\frac{y}{1 - y})

= lo g_{e} (y) + lo g_{e} (\frac{y}{- y + 1})

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (y) + lo g_{e} (\frac{y}{- y + 1})

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (y) + ln (\frac{y}{- y + 1})

ln (4 \cdot 5)

lo g_{10} (x^{2} + 3 x + 2) - lo g_{10} (x + 1)

2 lo g_{3} (u) + 7 lo g_{3} (v)

lo g_{10} (\frac{c ^{3}}{a ^{2} b ^{3}})

lo g_{10} (\frac{x ^{2} + 1}{x + 3})

What is expand log_{e}(ysqrt(y/(1-y))) ?
The solution to expand log_{e}(ysqrt(y/(1-y))) is ln(y)+ln(sqrt(y/(1-y)))