What is x+ln((x^2)/((x+1)^6)) ?

The solution to x+ln((x^2)/((x+1)^6)) is x++2ln(x)-6ln(x+1)

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simplify x+ln((x^2)/((x+1)^6))

simplify

x + ln (\frac{x ^{2}}{( x + 1 ) ^{6}})

x + + 2 ln (x) - 6 ln (x + 1)

Solution steps

x + ln (\frac{x ^{2}}{( x + 1 ) ^{6}})

Apply log rule:

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

ln (\frac{x ^{2}}{( x + 1 ) ^{6}}) = ln (x^{2}) - ln ((x + 1)^{6})

= x + + ln (x^{2}) - ln ((x + 1)^{6})

Apply log rule:

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

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

= x + + 2 ln (x) - ln ((x + 1)^{6})

Apply log rule:

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

ln ((x + 1)^{6}) = 6 ln (x + 1)

= x + + 2 ln (x) - 6 ln (x + 1)

lo g_{\frac{4 π ( m ^{3} )}{3}} (2 m)

ln (2 (ln (x) - 1))

20 lo g_{10} (\frac{0.05}{4 π \cdot 8 \cdot 1 0 ^{3}}) + 8 + 8

5 \cdot lo g_{10} (x) + 7 \cdot lo g_{10} (y)

3 ln (x) + \frac{1}{x} + ln (x + 1) + c

What is x+ln((x^2)/((x+1)^6)) ?
The solution to x+ln((x^2)/((x+1)^6)) is x++2ln(x)-6ln(x+1)