What is log_{e}(6x^2-2)-log_{e}(x^2) ?

The solution to log_{e}(6x^2-2)-log_{e}(x^2) is ln((6x^2-2)/(x^2))

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simplify log_{e}(6x^2-2)-log_{e}(x^2)

simplify

lo g_{e} (6 x^{2} - 2) - lo g_{e} (x^{2})

ln (\frac{6 x ^{2} - 2}{x ^{2}})

Solution steps

lo g_{e} (6 x^{2} - 2) - lo g_{e} (x^{2})

Apply log rule:

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

lo g_{e} (6 x^{2} - 2) - lo g_{e} (x^{2}) = lo g_{e} (\frac{6 x ^{2} - 2}{x ^{2}})

= lo g_{e} (\frac{6 x ^{2} - 2}{x ^{2}})

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (\frac{6 x ^{2} - 2}{x ^{2}})

\frac{1}{3} ln (2 x + 1) + \frac{1}{2} [ln (x - 4) - ln (x^{2} + 5)]

- lo g_{10} (5 (1 0^{- 2}))

ln (1 + n^{2}) - ln (n)

ln (\frac{1643.85}{821.85}) \cdot 8

ln - \frac{m g}{b} + a - ln (\frac{∣ m ∣ ∣ g ∣}{∣ b ∣})

What is log_{e}(6x^2-2)-log_{e}(x^2) ?
The solution to log_{e}(6x^2-2)-log_{e}(x^2) is ln((6x^2-2)/(x^2))