What is ln(ysqrt(y/(8-y))) ?

The solution to ln(ysqrt(y/(8-y))) is ln(y)+ln(sqrt(y/(8-y)))

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simplify ln(ysqrt(y/(8-y)))

simplify

ln (y \frac{y}{8 - y})

ln (y) + ln (\frac{y}{8 - y})

Solution steps

ln (y \frac{y}{8 - y})

Apply log rule:

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

ln (y \frac{y}{8 - y}) = ln (y) + ln (\frac{y}{8 - y})

= ln (y) + ln (\frac{y}{- y + 8})

\frac{1}{2} (ln (8) x^{2} - ln (4) - 3 ln (x) - ln (y))

lo g_{3} (x) - lo g_{3} (y) - lo g_{3} (z)

5 lo g_{b} (x) + 6 lo g_{b} (z)

lo g_{10} (3) 2

What is ln(ysqrt(y/(8-y))) ?
The solution to ln(ysqrt(y/(8-y))) is ln(y)+ln(sqrt(y/(8-y)))