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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 - \frac{1}{2} lo g_{10} (x) - 2 lo g_{10} (y)

\frac{3 ln ( 7 ) + 7 ln ( 2 )}{ln ( 7 ) - 2 ln ( 2 )} - 0

3 lo g_{2} (x) - 2 lo g_{2} (y) + \frac{1}{2} lo g_{2} (z)

ln (12) - ln (25)

lo g_{e} (2 e^{+ e})

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