What is ln(e^{x^2}sqrt(cos(5x-7))) ?

The solution to ln(e^{x^2}sqrt(cos(5x-7))) is x^2+ln(sqrt(cos(5x-7)))

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simplify ln(e^{x^2}sqrt(cos(5x-7)))

simplify

ln (e^{x^{2}} cos (5 x - 7))

x^{2} + ln (cos (5 x - 7))

Solution steps

ln (e^{x^{2}} cos (5 x - 7))

Apply log rule:

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

ln (e^{x^{2}} cos (5 x - 7)) = ln (e^{x^{2}}) + ln (cos (5 x - 7))

= ln (e^{x^{2}}) + ln (cos (5 x - 7))

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 (5 x - 7))

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

= x^{2} + ln (cos (5 x - 7))

lo g_{3} (8) + lo g_{3} (x) - 2 lo g_{3} (x + 4)

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

ln (\frac{11}{3})

ln (\frac{e}{a})

ln (\frac{p}{1 - p})

What is ln(e^{x^2}sqrt(cos(5x-7))) ?
The solution to ln(e^{x^2}sqrt(cos(5x-7))) is x^2+ln(sqrt(cos(5x-7)))