What is ln(z^2+5)-ln(z^2-4) ?

The solution to ln(z^2+5)-ln(z^2-4) is ln((z^2+5)/(z^2-4))

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simplify ln(z^2+5)-ln(z^2-4)

simplify

ln (z^{2} + 5) - ln (z^{2} - 4)

ln (\frac{z ^{2} + 5}{z ^{2} - 4})

Solution steps

ln (z^{2} + 5) - ln (z^{2} - 4)

Apply log rule:

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

ln (z^{2} + 5) - ln (z^{2} - 4) = ln (\frac{z ^{2} + 5}{z ^{2} - 4})

= ln (\frac{z ^{2} + 5}{z ^{2} - 4})

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What is ln(z^2+5)-ln(z^2-4) ?
The solution to ln(z^2+5)-ln(z^2-4) is ln((z^2+5)/(z^2-4))