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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

Simplify

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

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

(1.3)^{2} + ln (1.3) - ln (2 e^{1})

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

\frac{1}{59049} \cdot ln^{- 1} (\frac{1}{3})

- \frac{1}{0.22} ln (\frac{1}{150})

ln (\frac{x + 4}{2})

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