What is ln(x^2(e^{3x}+e^{-3x})) ?

The solution to ln(x^2(e^{3x}+e^{-3x})) is 2ln(x)+ln(e^{3x}+e^{-3x})

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simplify ln(x^2(e^{3x}+e^{-3x}))

simplify

ln (x^{2} (e^{3 x} + e^{- 3 x}))

2 ln (x) + ln (e^{3 x} + e^{- 3 x})

Solution steps

ln (x^{2} (e^{3 x} + e^{- 3 x}))

Apply log rule:

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

ln (x^{2} (e^{3 x} + e^{- 3 x})) = ln (x^{2}) + ln (e^{3 x} + e^{- 3 x})

= ln (x^{2}) + ln (e^{3 x} + e^{- 3 x})

Apply log rule:

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

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

= 2 ln (x) + ln (e^{3 x} + e^{- 3 x})

5 lo g_{3} (x) - 2 lo g_{3} (y)

\frac{1}{5} lo g_{3} (2)

ln ∣ x - 2 ∣ + ln ∣ x + 5 ∣ + C

2 ln (\frac{20 + 409}{3})

2 ln (2 + 1)

What is ln(x^2(e^{3x}+e^{-3x})) ?
The solution to ln(x^2(e^{3x}+e^{-3x})) is 2ln(x)+ln(e^{3x}+e^{-3x})