What is ln(1/2 |x+2+sqrt(x^2+4x+8)|) ?

The solution to ln(1/2 |x+2+sqrt(x^2+4x+8)|) is ln|x+sqrt(x^2+4x+8)+2|-ln(2)

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simplify ln(1/2 |x+2+sqrt(x^2+4x+8)|)

simplify

ln (\frac{1}{2} x + 2 + x^{2} + 4 x + 8)

ln x + x^{2} + 4 x + 8 + 2 - ln (2)

Solution steps

ln (\frac{1}{2} x + 2 + x^{2} + 4 x + 8)

Apply log rule:

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

ln (\frac{1}{2} x + 2 + x^{2} + 4 x + 8) = ln (\frac{1}{2}) + ln x + 2 + x^{2} + 4 x + 8

= ln (\frac{1}{2}) + ln x + x^{2} + 4 x + 8 + 2

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} + 4 x + 8 + 2

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2) + ln x + x^{2} + 4 x + 8 + 2

0 - ln (2) + ln x + 2 + x^{2} + 4 x + 8 = - ln (2) + ln x + 2 + x^{2} + 4 x + 8

= ln x + x^{2} + 4 x + 8 + 2 - ln (2)

4 lo g_{e} (8) - 4 lo g_{e} (4)

ln (50 e^{x})

lo g_{2} ((\frac{x}{y})^{5})

ln (\frac{0.5}{- 0.15})

ln (1 + e^{- x}) - ln (1 + e^{x})

What is ln(1/2 |x+2+sqrt(x^2+4x+8)|) ?
The solution to ln(1/2 |x+2+sqrt(x^2+4x+8)|) is ln|x+sqrt(x^2+4x+8)+2|-ln(2)