What is ln(x^2-9)-ln(4-x^2) ?

The solution to ln(x^2-9)-ln(4-x^2) is ln((x^2-9)/(4-x^2))

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simplify ln(x^2-9)-ln(4-x^2)

simplify

ln (x^{2} - 9) - ln (4 - x^{2})

ln (\frac{x ^{2} - 9}{4 - x ^{2}})

Solution steps

ln (x^{2} - 9) - ln (4 - x^{2})

Apply log rule:

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

ln (x^{2} - 9) - ln (4 - x^{2}) = ln (\frac{x ^{2} - 9}{- x ^{2} + 4})

= ln (\frac{x ^{2} - 9}{4 - x ^{2}})

ln ∣ x ∣ + ln ∣ y ∣

\frac{1}{2} lo g_{2} (x) + lo g_{2} (y)

\frac{1}{2} lo g_{10} (9) + 3 lo g_{10} (2)

- \frac{1}{3} ln (8) + 2 ln (5)

\frac{1}{2} ln (x) + 8 ln (y) - 7 ln (z)

What is ln(x^2-9)-ln(4-x^2) ?
The solution to ln(x^2-9)-ln(4-x^2) is ln((x^2-9)/(4-x^2))