What is ln((sqrt(x+1))/(xy)) ?

The solution to ln((sqrt(x+1))/(xy)) is ln(sqrt(x+1))-ln(x)-ln(y)

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simplify ln((sqrt(x+1))/(xy))

simplify

ln (\frac{x + 1}{x y})

ln (x + 1) - ln (x) - ln (y)

Solution steps

ln (\frac{x + 1}{x y})

Apply log rule:

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

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

= ln (x + 1) - ln (x y)

Apply log rule:

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

ln (x y) = ln (x) + ln (y)

= ln (x + 1) - (ln (x) + ln (y))

- (ln (x) + ln (y)) : - ln (x) - ln (y)

= ln (x + 1) - ln (x) - ln (y)

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

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

- ln (y + 1) - ln (x)

ln (\frac{469}{94.5})

ln (- 2 e^{x})

What is ln((sqrt(x+1))/(xy)) ?
The solution to ln((sqrt(x+1))/(xy)) is ln(sqrt(x+1))-ln(x)-ln(y)