What is log_{e}((x^2+4)/(x^2-4)) ?

The solution to log_{e}((x^2+4)/(x^2-4)) is ln(x^2+4)-ln(x^2-4)

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simplify log_{e}((x^2+4)/(x^2-4))

simplify

lo g_{e} (\frac{x ^{2} + 4}{x ^{2} - 4})

ln (x^{2} + 4) - ln (x^{2} - 4)

Solution steps

lo g_{e} (\frac{x ^{2} + 4}{x ^{2} - 4})

Apply log rule:

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

lo g_{e} (\frac{x ^{2} + 4}{x ^{2} - 4}) = lo g_{e} (x^{2} + 4) - lo g_{e} (x^{2} - 4)

= lo g_{e} (x^{2} + 4) - lo g_{e} (x^{2} - 4)

Apply log rule:

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

= ln (x^{2} + 4) - lo g_{e} (x^{2} - 4)

Apply log rule:

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

= ln (x^{2} + 4) - ln (x^{2} - 4)

ln (3 e^{x})

ln (\frac{3}{81})

3.15 + lo g_{10} (\frac{1.875}{0.625})

\frac{1}{2} (ln (5) - ln (4))

- 3 ln ∣ x + 2 ∣ + 4 ln ∣ x + 3 ∣

What is log_{e}((x^2+4)/(x^2-4)) ?
The solution to log_{e}((x^2+4)/(x^2-4)) is ln(x^2+4)-ln(x^2-4)