What is ln(1/(xsqrt(x+1))) ?

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

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simplify ln(1/(xsqrt(x+1)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x x + 1) = ln (x) + ln (x + 1)

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

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (x) + ln (x + 1))

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

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

lo g_{10} (\frac{1000}{x ^{2} + y ^{2}})

lo g_{10} (3 x^{5})

ln (\frac{x ^{2}}{25})

- lo g_{10} (1.3 \cdot 1 0^{- 7})

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