What is ln((x^{1/2})/(x+1)) ?

The solution to ln((x^{1/2})/(x+1)) is 1/2 ln(x)-ln(x+1)

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simplify ln((x^{1/2})/(x+1))

simplify

ln (\frac{x ^{\frac{1}{2}}}{x + 1})

\frac{1}{2} ln (x) - ln (x + 1)

Solution steps

ln (\frac{x ^{\frac{1}{2}}}{x + 1})

Apply log rule:

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

ln (\frac{x ^{\frac{1}{2}}}{x + 1}) = ln (x^{\frac{1}{2}}) - ln (x + 1)

= ln (x^{\frac{1}{2}}) - ln (x + 1)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (x^{\frac{1}{2}}) = \frac{1}{2} ln (x)

= \frac{1}{2} ln (x) - ln (x + 1)

- lo g_{10} (8.76275 \cdot 1 0^{- 6})

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

20 \cdot lo g_{10} (\frac{4 \cdot π \cdot 2}{0.46})

7.952707 ln (6000 x^{0.8})

ln (\frac{e ^{x}}{x ( x + 3 ) ^{2}})

What is ln((x^{1/2})/(x+1)) ?
The solution to ln((x^{1/2})/(x+1)) is 1/2 ln(x)-ln(x+1)