What is ln(x^2(x-1)(x^2+4)^3) ?

The solution to ln(x^2(x-1)(x^2+4)^3) is 2ln(x)+ln(x-1)+3ln(x^2+4)

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simplify ln(x^2(x-1)(x^2+4)^3)

simplify

ln (x^{2} (x - 1) (x^{2} + 4)^{3})

2 ln (x) + ln (x - 1) + 3 ln (x^{2} + 4)

Solution steps

ln (x^{2} (x - 1) (x^{2} + 4)^{3})

Apply log rule:

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

ln (x^{2} (x - 1) (x^{2} + 4)^{3}) = ln (x^{2}) + ln (x - 1) + ln ((x^{2} + 4)^{3})

= ln (x^{2}) + ln (x - 1) + ln ((x^{2} + 4)^{3})

Apply log rule:

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

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

= 2 ln (x) + ln (x - 1) + ln ((x^{2} + 4)^{3})

Apply log rule:

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

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

= 2 ln (x) + ln (x - 1) + 3 ln (x^{2} + 4)

ln (17 x^{- 3} y)

\frac{27}{5} ln (2) - \frac{9}{5} ln (3)

ln (e x^{4}) + 4

ln (\frac{5 x ^{6}}{11 y ^{7}})

[\frac{( 8.314 \cdot 293 )}{( 2 \cdot 96485 )}] \cdot ln (\frac{1}{0.05})

What is ln(x^2(x-1)(x^2+4)^3) ?
The solution to ln(x^2(x-1)(x^2+4)^3) is 2ln(x)+ln(x-1)+3ln(x^2+4)