What is ln(ysqrt(y/(7-y))) ?

The solution to ln(ysqrt(y/(7-y))) is ln(y)+ln(sqrt(y/(7-y)))

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simplify ln(ysqrt(y/(7-y)))

simplify

ln (y \frac{y}{7 - y})

ln (y) + ln (\frac{y}{7 - y})

Solution steps

ln (y \frac{y}{7 - y})

Apply log rule:

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

ln (y \frac{y}{7 - y}) = ln (y) + ln (\frac{y}{7 - y})

= ln (y) + ln (\frac{y}{- y + 7})

\frac{1}{4 ( 1 + x ^{4} )} + ln (x) - \frac{1}{4} ln (1 + x^{4})

- lo g_{10} (3.16 \cdot 1 0^{- 8})

ln (4) + ln (8)

- lo g_{10} (3.5 \times 1 0^{- 4})

What is ln(ysqrt(y/(7-y))) ?
The solution to ln(ysqrt(y/(7-y))) is ln(y)+ln(sqrt(y/(7-y)))