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

The solution to ln((2x-1)/2)+sqrt(((2x-1)/2)^2+1/2) is ln(2x-1)-ln(2)+(sqrt(4x^2-4x+3))/2

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

simplify

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

ln (2 x - 1) - ln (2) + \frac{4 x ^{2} - 4 x + 3}{2}

Solution steps

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

Apply log rule:

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

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

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

(\frac{2 x - 1}{2})^{2} + \frac{1}{2} = \frac{4 x ^{2} - 4 x + 3}{2}

= ln (2 x - 1) - ln (2) + \frac{4 x ^{2} - 4 x + 3}{2}

lo g_{6} (\frac{216 x ^{3}}{y})

\frac{1}{20} ln (\frac{31}{20})

ln (2.8246 x 1 0^{- 10})

ln (- iπ)

lo g_{3} (w \cdot u^{6} \cdot v)

What is ln((2x-1)/2)+sqrt(((2x-1)/2)^2+1/2) ?
The solution to ln((2x-1)/2)+sqrt(((2x-1)/2)^2+1/2) is ln(2x-1)-ln(2)+(sqrt(4x^2-4x+3))/2