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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

lo g_{2} (8) - lo g_{2} (x) - lo g_{2} (y)

lo g_{10} (2) + lo g_{10} (3)

lo g_{10} (10 x)

2 lo g_{10} (x) - 3 lo g_{10} (y) + 4 lo g_{10} (z)

lo g_{10} (2 x)

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