What is ln(e^{4x}arctan(x^2)) ?

The solution to ln(e^{4x}arctan(x^2)) is 4x+ln(arctan(x^2))

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simplify ln(e^{4x}arctan(x^2))

simplify

ln (e^{4 x} arctan (x^{2}))

4 x + ln (arctan (x^{2}))

Solution steps

ln (e^{4 x} arctan (x^{2}))

Apply log rule:

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

ln (e^{4 x} arctan (x^{2})) = ln (e^{4 x}) + ln (arctan (x^{2}))

= ln (e^{4 x}) + ln (arctan (x^{2}))

Apply log rule:

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

ln (e^{4 x}) = 4 x ln (e)

= 4 x ln (e) + ln (arctan (x^{2}))

4 x ln (e) = 4 x

= 4 x + ln (arctan (x^{2}))

ln (4) + 3 ln (3)

lo g_{e} (5 e^{2 x})

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

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

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

What is ln(e^{4x}arctan(x^2)) ?
The solution to ln(e^{4x}arctan(x^2)) is 4x+ln(arctan(x^2))