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

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

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simplify ln((x^2)/(sqrt(1+x)))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{2}) = 2 ln (x)

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

9 ln (x) - 3 ln (2 x^{3})

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

f (x) = ln (x^{3} e^{- 3 x})

lo g_{10} (\frac{- 5}{x + 8})

ln (x) - \frac{1}{4} ln (v^{2} + 2)

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