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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln ((x^{2} + 5)^{5}) = 5 ln (x^{2} + 5)

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

Apply log rule:

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

ln ((1 - x^{4})^{4}) = 4 ln (1 - x^{4})

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

lo g_{3} (11 z)

lo g_{9} (\frac{g}{81})

ln (3 x y^{2})

3 ln (x) + 2 ln (y) + ln (5)

lo g_{10} (\frac{4 x ^{3}}{y ^{2}})

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