What is (ln(x))/2+ln(sqrt(3-x))-ln(sqrt(2)) ?

The solution to (ln(x))/2+ln(sqrt(3-x))-ln(sqrt(2)) is (ln(x))/2+ln(sqrt((3-x)/2))

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simplify (ln(x))/2+ln(sqrt(3-x))-ln(sqrt(2))

simplify

\frac{ln ( x )}{2} + ln (3 - x) - ln (2)

\frac{ln ( x )}{2} + ln (\frac{3 - x}{2})

Solution steps

\frac{ln ( x )}{2} + ln (3 - x) - ln (2)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (3 - x) - ln (2) = ln (\frac{- x + 3}{2})

= \frac{ln ( x )}{2} + ln (\frac{- x + 3}{2})

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \frac{ln ( x )}{2} + ln (\frac{3 - x}{2})

ln (7 - 3) - ln (2 - 3)

- lo g_{10} (1.99 \cdot 1 0^{- 4})

ln (\frac{1}{0.995})

ln (y + 1) - ln (x)

What is (ln(x))/2+ln(sqrt(3-x))-ln(sqrt(2)) ?
The solution to (ln(x))/2+ln(sqrt(3-x))-ln(sqrt(2)) is (ln(x))/2+ln(sqrt((3-x)/2))