What is 1/2 ln|1+x^2|+ln|y| ?

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

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simplify 1/2 ln|1+x^2|+ln|y|

simplify

\frac{1}{2} ln 1 + x^{2} + ln ∣ y ∣

ln (1 + x^{2}^{\frac{1}{2}} ∣ y ∣)

Solution steps

\frac{1}{2} ln 1 + x^{2} + ln ∣ y ∣

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (1 + x^{2}^{\frac{1}{2}} ∣ y ∣)

ln (2 sec (x))

ln (\frac{- 1}{0 - 2})

150 ln (\frac{350}{400 - 100})

2 lo g_{10} (x) - lo g_{10} (x + 6)

- lo g_{10} (6.5 \cdot 1 0^{- 12})

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