What is ln((2x^4)/((x+1)^9)) ?

The solution to ln((2x^4)/((x+1)^9)) is ln(2)+4ln(x)-9ln(x+1)

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simplify ln((2x^4)/((x+1)^9))

simplify

ln (\frac{2 x ^{4}}{( x + 1 ) ^{9}})

ln (2) + 4 ln (x) - 9 ln (x + 1)

Solution steps

ln (\frac{2 x ^{4}}{( x + 1 ) ^{9}})

Apply log rule:

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

ln (\frac{2 x ^{4}}{( x + 1 ) ^{9}}) = ln (2 x^{4}) - ln ((x + 1)^{9})

= ln (2 x^{4}) - ln ((x + 1)^{9})

Apply log rule:

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

ln ((x + 1)^{9}) = 9 ln (x + 1)

= ln (2 x^{4}) - 9 ln (x + 1)

Apply log rule:

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

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

= ln (2) + ln (x^{4}) - 9 ln (x + 1)

Apply log rule:

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

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

= ln (2) + 4 ln (x) - 9 ln (x + 1)

- 8.314 \cdot ln (\frac{1}{10})

\frac{1}{2} ln (\frac{2}{3})

ln (18) - ln (8)

lo g_{7} (19 w)

ln (x) - ln (ux)

What is ln((2x^4)/((x+1)^9)) ?
The solution to ln((2x^4)/((x+1)^9)) is ln(2)+4ln(x)-9ln(x+1)