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

The solution to ln(x^4-4)-ln(x^2+2) is ln((x+sqrt(2))(x-sqrt(2)))

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

simplify

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

ln ((x + 2) (x - 2))

Solution steps

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

Apply log rule:

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

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

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

Simplify

\frac{x ^{4} - 4}{x ^{2} + 2} : (x + 2) (x - 2)

= ln ((x + 2) (x - 2))

lo g_{3} (x + 25) - lo g_{3} (x - 1)

lo g_{4} (x^{2} - 4) - 6 lo g_{4} (x + 2)

ln (4 x^{2}) + ln (3 x^{3})

\frac{1}{6} ln (y) + ln (z)

lo g_{10} (48) + lo g_{10} (75)

What is ln(x^4-4)-ln(x^2+2) ?
The solution to ln(x^4-4)-ln(x^2+2) is ln((x+sqrt(2))(x-sqrt(2)))