What is ln(((3y+1)^5)/(sqrt(y^2+1))) ?

The solution to ln(((3y+1)^5)/(sqrt(y^2+1))) is 5ln(3y+1)-ln(sqrt(y^2+1))

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simplify ln(((3y+1)^5)/(sqrt(y^2+1)))

simplify

ln (\frac{( 3 y + 1 ) ^{5}}{y ^{2} + 1})

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

Solution steps

ln (\frac{( 3 y + 1 ) ^{5}}{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 ) ^{5}}{y ^{2} + 1}) = ln ((3 y + 1)^{5}) - ln (y^{2} + 1)

= ln ((3 y + 1)^{5}) - ln (y^{2} + 1)

Apply log rule:

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

ln ((3 y + 1)^{5}) = 5 ln (3 y + 1)

= 5 ln (3 y + 1) - ln (y^{2} + 1)

ln (b) + \frac{ln ( c )}{2} - 3 ln (d)

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

ln \frac{x}{2} + 1 + ln \frac{x}{2} - 1

2000 ln (\frac{5}{4})

2 ln (x y)

What is ln(((3y+1)^5)/(sqrt(y^2+1))) ?
The solution to ln(((3y+1)^5)/(sqrt(y^2+1))) is 5ln(3y+1)-ln(sqrt(y^2+1))