What is 1/2 ln|2+2v^2|-1/2 arctan(v)+ln(x) ?

The solution to 1/2 ln|2+2v^2|-1/2 arctan(v)+ln(x) is ln(|2+2v^2|^{1/2}x)-1/2 arctan(v)

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simplify 1/2 ln|2+2v^2|-1/2 arctan(v)+ln(x)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

lo g_{7} (3 k)

lo g_{10} (2) + lo g_{10} (4) + lo g_{10} (8)

lo g_{10} (a^{2} b)

ln (1 0^{- 5} \cdot 0.082 \cdot 298)

7 lo g_{2} (r) - 8 lo g_{2} (s) - 2 lo g_{2} (t)

What is 1/2 ln|2+2v^2|-1/2 arctan(v)+ln(x) ?
The solution to 1/2 ln|2+2v^2|-1/2 arctan(v)+ln(x) is ln(|2+2v^2|^{1/2}x)-1/2 arctan(v)