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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= lo g_{e} (\frac{x ^{2}}{lo g _{e} ( x )})

Simplify

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

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

Apply log rule:

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

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

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

- 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)

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