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

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

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

simplify

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

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

Solution steps

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

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

Apply log rule:

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

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

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

lo g_{10} (3) - lo g_{10} (4)

ln (\frac{( 1 + 5 )}{2})

4 lo g_{10} (x) + 7 lo g_{10} (y)

lo g_{5} (\frac{25}{x + 3})

2 ln (ln (e^{z}) ln (e^{y})) - ln (x^{2})

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