What is ln((x^4+5)(x^2-1)^2) ?

The solution to ln((x^4+5)(x^2-1)^2) is ln(x^4+5)+2ln(x^2-1)

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simplify ln((x^4+5)(x^2-1)^2)

simplify

ln ((x^{4} + 5) (x^{2} - 1)^{2})

ln (x^{4} + 5) + 2 ln (x^{2} - 1)

Solution steps

ln ((x^{4} + 5) (x^{2} - 1)^{2})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln ((x^{4} + 5) (x^{2} - 1)^{2}) = ln (x^{4} + 5) + ln ((x^{2} - 1)^{2})

= ln (x^{4} + 5) + ln ((x^{2} - 1)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x^{2} - 1)^{2}) = 2 ln (x^{2} - 1)

= ln (x^{4} + 5) + 2 ln (x^{2} - 1)

5 ln (x) + 6 ln (y) + 9 ln (z)

ln (\frac{1}{y ^{2} - 1})

ln (4.64) - ln (10.733)

182000 \cdot [ln (0.4) - ln (1.3)]

2 + 2 lo g_{10} (x) - \frac{3}{2} lo g_{10} (y)

What is ln((x^4+5)(x^2-1)^2) ?
The solution to ln((x^4+5)(x^2-1)^2) is ln(x^4+5)+2ln(x^2-1)