What is ln(1/2 sqrt(x^2-4)) ?

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

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simplify ln(1/2 sqrt(x^2-4))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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^{2} - 4)

Apply log rule:

lo g_{a} (1) = 0

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

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

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

- ln ∣ x - 3 ∣ + 2 ln ∣ x - 2 ∣ + C

ln (\frac{x ^{4}}{y ^{5}})

\frac{1}{2} ln (4 + 15)

ln (\frac{- 4.92}{4.79526})

e^{- 2} - ln (\frac{3}{7})

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