What is ln(1/2 |x-3+sqrt(x^2-6x+13)|) ?

The solution to ln(1/2 |x-3+sqrt(x^2-6x+13)|) is ln|x+sqrt(x^2-6x+13)-3|-ln(2)

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simplify ln(1/2 |x-3+sqrt(x^2-6x+13)|)

simplify

ln (\frac{1}{2} x - 3 + x^{2} - 6 x + 13)

ln x + x^{2} - 6 x + 13 - 3 - ln (2)

Solution steps

ln (\frac{1}{2} x - 3 + x^{2} - 6 x + 13)

Apply log rule:

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

ln (\frac{1}{2} x - 3 + x^{2} - 6 x + 13) = ln (\frac{1}{2}) + ln x - 3 + x^{2} - 6 x + 13

= ln (\frac{1}{2}) + ln x + x^{2} - 6 x + 13 - 3

Apply log rule:

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

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

= ln (1) - ln (2) + ln x + x^{2} - 6 x + 13 - 3

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2) + ln x + x^{2} - 6 x + 13 - 3

0 - ln (2) + ln x - 3 + x^{2} - 6 x + 13 = - ln (2) + ln x - 3 + x^{2} - 6 x + 13

= ln x + x^{2} - 6 x + 13 - 3 - ln (2)

3 lo g_{9} (a) - 12 lo g_{9} (b)

3 ln ∣ x ∣ - 2 ln ∣ x + 11 ∣

\frac{3}{2} ln (t) + \frac{1}{2} ln (b) - 2 + ln (e^{2}) - 8 ln (m)

ln (800 e^{0.05 t}) - ln (220 e^{- 0.05 t})

ln (e^{4 x} x^{7})

What is ln(1/2 |x-3+sqrt(x^2-6x+13)|) ?
The solution to ln(1/2 |x-3+sqrt(x^2-6x+13)|) is ln|x+sqrt(x^2-6x+13)-3|-ln(2)