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

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

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

simplify

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

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

Solution steps

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

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

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})

Remove parentheses:

(a) = a

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

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

ln^{2} (\frac{1}{3}) - (ln (\frac{1}{3}))^{2}

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

ln (sin (x)) + ln (x + y)

13 ln (\frac{208}{3}) + 7 ln (80 - 0.75 \cdot \frac{208}{3})

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