What is ln(ysqrt(y/(6-y))) ?

The solution to ln(ysqrt(y/(6-y))) is ln(y)+ln(sqrt(y/(6-y)))

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simplify ln(ysqrt(y/(6-y)))

simplify

ln (y \frac{y}{6 - y})

ln (y) + ln (\frac{y}{6 - y})

Solution steps

ln (y \frac{y}{6 - y})

Apply log rule:

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

ln (y \frac{y}{6 - y}) = ln (y) + ln (\frac{y}{6 - y})

= ln (y) + ln (\frac{y}{- y + 6})

2 ln (x - 2) - ln (x - 1)

lo g_{10} (\frac{1}{u ^{2} + v ^{2}})

lo g_{10} (x) - 2 \cdot lo g_{10} (y) + 5 \cdot lo g_{10} (z)

lo g_{4} (2) + lo g_{4} (x)

lo g_{3} (\frac{27}{x + 4})

What is ln(ysqrt(y/(6-y))) ?
The solution to ln(ysqrt(y/(6-y))) is ln(y)+ln(sqrt(y/(6-y)))