What is 1/3 ln((x(x+1))/((y+1)^3)) ?

The solution to 1/3 ln((x(x+1))/((y+1)^3)) is 1/3 ln(x(x+1))-ln(y+1)

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simplify 1/3 ln((x(x+1))/((y+1)^3))

simplify

\frac{1}{3} ln (\frac{x ( x + 1 )}{( y + 1 ) ^{3}})

\frac{1}{3} ln (x (x + 1)) - ln (y + 1)

Solution steps

\frac{1}{3} ln (\frac{x ( x + 1 )}{( y + 1 ) ^{3}})

Apply log rule:

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

ln (\frac{x ( x + 1 )}{( y + 1 ) ^{3}}) = ln (x (x + 1)) - ln ((y + 1)^{3})

= \frac{1}{3} (ln (x (x + 1)) - ln ((y + 1)^{3}))

Apply log rule:

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

ln ((y + 1)^{3}) = 3 ln (y + 1)

= \frac{1}{3} (ln (x (x + 1)) - 3 ln (y + 1))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{3}, b = ln (x (x + 1)), c = 3 ln (y + 1)

= \frac{1}{3} ln (x (x + 1)) - \frac{1}{3} \cdot 3 ln (y + 1)

= \frac{1}{3} ln (x (x + 1)) - 3 \cdot \frac{1}{3} ln (y + 1)

3 \cdot \frac{1}{3} ln (y + 1) = ln (y + 1)

= \frac{1}{3} ln (x (x + 1)) - ln (y + 1)

22 ln (\frac{125}{11}) + 62 + 25 ln (30) + 15 ln (\frac{250}{3})

a pp ro x ima t e (\frac{4}{5} lo g_{2} (\frac{4}{5}))

ln (\frac{3 e ^{- n^{3} + n x}}{x})

ln ∣ x ∣ - ln x^{2} + 1

lo g_{10} (\frac{( 2 sin ( x ) )}{sin ( 2 x )})

What is 1/3 ln((x(x+1))/((y+1)^3)) ?
The solution to 1/3 ln((x(x+1))/((y+1)^3)) is 1/3 ln(x(x+1))-ln(y+1)