What is join 1/2 ln(2pi+sqrt(4pi^2+1)) ?

The solution to join 1/2 ln(2pi+sqrt(4pi^2+1)) is ln((2pi+sqrt(4pi^2+1))^{1/2})

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join 1/2 ln(2pi+sqrt(4pi^2+1))

join

\frac{1}{2} ln (2 π + 4 π^{2} + 1)

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

Decimal Notation

1.26864 \dots

Solution steps

\frac{1}{2} ln (2 π + 4 π^{2} + 1)

Apply log rule:

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

\frac{1}{2} ln (2 π + 4 π^{2} + 1) = ln ((2 π + 4 π^{2} + 1)^{\frac{1}{2}})

= ln ((2 π + 4 π^{2} + 1)^{\frac{1}{2}})

lo g_{10} (x^{3} y^{5})

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

lo g_{5} (\frac{y}{7})

ln (\frac{e ^{2} + e ^{4} - 1}{2 + 5})

ln (0.6339 π)

What is join 1/2 ln(2pi+sqrt(4pi^2+1)) ?
The solution to join 1/2 ln(2pi+sqrt(4pi^2+1)) is ln((2pi+sqrt(4pi^2+1))^{1/2})