What is ln((e^{X^2}cos(X))/(sqrt(2X))) ?

The solution to ln((e^{X^2}cos(X))/(sqrt(2X))) is X^2+ln(cos(X))-ln(sqrt(2)sqrt(X))

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simplify ln((e^{X^2}cos(X))/(sqrt(2X)))

simplify

ln (\frac{e ^{X^{2}} cos ( X )}{2 X})

X^{2} + ln (cos (X)) - ln (2 X)

Solution steps

ln (\frac{e ^{X^{2}} cos ( X )}{2 X})

Apply log rule:

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

ln (\frac{e ^{X^{2}} cos ( X )}{2 X}) = ln (e^{X^{2}} cos (X)) - ln (2 X)

= ln (e^{X^{2}} cos (X)) - ln (2 X)

Apply log rule:

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

ln (e^{X^{2}} cos (X)) = ln (e^{X^{2}}) + ln (cos (X))

= ln (e^{X^{2}}) + ln (cos (X)) - ln (2 X)

Apply log rule:

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

ln (e^{X^{2}}) = X^{2} ln (e)

= X^{2} ln (e) + ln (cos (X)) - ln (2 X)

X^{2} ln (e) = X^{2}

ln (2 X) = ln (2 X)

= X^{2} + ln (cos (X)) - ln (2 X)

\frac{1}{2} (ln (6) + ln (2))

lo g_{e} (\frac{( 4300 )}{3})

ln (\frac{190 ( 200 - 190 )}{3600})

10.64 + lo g_{10} (\frac{0.1}{0.175})

What is ln((e^{X^2}cos(X))/(sqrt(2X))) ?
The solution to ln((e^{X^2}cos(X))/(sqrt(2X))) is X^2+ln(cos(X))-ln(sqrt(2)sqrt(X))