What is simplify-ln(x+1)+1/2 ln(x) ?

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

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simplify-ln(x+1)+1/2 ln(x)

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

lo g_{2} (\frac{2}{12})

4 ln (x) - \frac{1}{5} ln (x^{4})

ln (v y) - ln (y) - 1

ln (40) - ln (60)

ln (x e^{1})

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