What is ln(((3y+1)^4)/(sqrt(y^2+1))) ?

The solution to ln(((3y+1)^4)/(sqrt(y^2+1))) is 4ln(3y+1)-ln(sqrt(y^2+1))

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simplify ln(((3y+1)^4)/(sqrt(y^2+1)))

simplify

ln (\frac{( 3 y + 1 ) ^{4}}{y ^{2} + 1})

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

Solution steps

ln (\frac{( 3 y + 1 ) ^{4}}{y ^{2} + 1})

Apply log rule:

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

ln (\frac{( 3 y + 1 ) ^{4}}{y ^{2} + 1}) = ln ((3 y + 1)^{4}) - ln (y^{2} + 1)

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

Apply log rule:

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

ln ((3 y + 1)^{4}) = 4 ln (3 y + 1)

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

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3 (ln (10) - ln (5))

ln (x (x + 4))

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