What is ln(ysqrt(y/(5-y))) ?

The solution to ln(ysqrt(y/(5-y))) is ln(y)+ln(sqrt(y/(5-y)))

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simplify ln(ysqrt(y/(5-y)))

simplify

ln (y \frac{y}{5 - y})

ln (y) + ln (\frac{y}{5 - y})

Solution steps

ln (y \frac{y}{5 - y})

Apply log rule:

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

ln (y \frac{y}{5 - y}) = ln (y) + ln (\frac{y}{5 - y})

= ln (y) + ln (\frac{y}{- y + 5})

lo g_{6} (x \cdot y \cdot z^{5})

π (3 \cdot ln (3) - 2 \cdot ln (2) + 1)

8 lo g_{6} (u) + 9 lo g_{6} (v)

lo g_{10} (\frac{y ^{5} x}{z})

lo g_{10} (\frac{y}{z ^{9}})

What is ln(ysqrt(y/(5-y))) ?
The solution to ln(ysqrt(y/(5-y))) is ln(y)+ln(sqrt(y/(5-y)))