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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{a}{2}) + ln (a^{3})

\frac{1}{4} lo g_{e} (y - 2) - \frac{1}{4} lo g_{e} (y + 2)

\frac{1}{2} ln 1 + x^{2} + \frac{1}{2} ln 1 + y^{2}

ln (K + 1) + ln (L + 1)

ln (x + 3) - 5 ln (x) + 4 ln (x - 2)

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