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

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

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simplify ln((e^{x^2})/(x^2))

simplify

ln (\frac{e ^{x^{2}}}{x ^{2}})

x^{2} - 2 ln (x)

Solution steps

ln (\frac{e ^{x^{2}}}{x ^{2}})

Apply log rule:

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

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

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

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 (x^{2})

Apply log rule:

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

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

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

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

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

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

ln (\frac{5 g ^{- 1}}{w})

- lo g_{10} (3.55 \cdot 1 0^{- 32})

(ln (b + 2 a) - ln (a)) k - (a + 2 b) (a + b)

8 ln (x + 6) - 5 ln (x)