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

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

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simplify log_{e}(x+2)-log_{e}(3x)

simplify

lo g_{e} (x + 2) - lo g_{e} (3 x)

ln (\frac{x + 2}{3 x})

Solution steps

lo g_{e} (x + 2) - lo g_{e} (3 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} (3 x) = lo g_{e} (\frac{x + 2}{3 x})

= lo g_{e} (\frac{x + 2}{3 x})

Apply log rule:

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

= ln (\frac{x + 2}{3 x})

ln ((x^{2} + 8 x + 7) (2 x^{2} - 16 x))

ln (\frac{15}{13 - 2 ( 1.5 )})

ln^{5} (\frac{( e ^{2} )}{5})

4.76 + lo g_{10} (\frac{1}{9})

7 lo g_{a} (y - 2) - 2 lo g_{a} (y + 3)

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