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

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

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

simplify

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

ln (x)

Solution steps

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

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

Cancel the common factor:

x

= lo g_{e} (x)

Apply log rule:

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

= ln (x)

ln (\frac{3.5}{1.5})

ln (2) - ln (\frac{3}{2})

ln (\frac{x}{x ^{2} - 4})

lo g_{2} (\frac{1}{0.1}) + 0.9

ln (x - 3) - ln (x)

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