What is ln((|x+sqrt(x^2-4)|)/2) ?

The solution to ln((|x+sqrt(x^2-4)|)/2) is ln|x+sqrt(x^2-4)|-ln(2)

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simplify ln((|x+sqrt(x^2-4)|)/2)

simplify

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

ln x + x^{2} - 4 - ln (2)

Solution steps

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

Apply log rule:

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

ln (\frac{x + x ^{2} - 4}{2}) = ln x + x^{2} - 4 - ln (2)

= ln x + x^{2} - 4 - ln (2)

ln (- 3 e^{2 x})

\frac{1}{3} lo g_{4} (y) - 3 lo g_{4} (x)

ln (\frac{7}{382})

\frac{1}{5} (ln (10 + 101) - ln (- 5 + 26))

\frac{1}{2} lo g_{10} (x) - 2 lo g_{10} (y)

What is ln((|x+sqrt(x^2-4)|)/2) ?
The solution to ln((|x+sqrt(x^2-4)|)/2) is ln|x+sqrt(x^2-4)|-ln(2)