What is ln(1/2 (x^2-6x+5)) ?

The solution to ln(1/2 (x^2-6x+5)) is ln(x^2-6x+5)-ln(2)

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simplify ln(1/2 (x^2-6x+5))

simplify

ln (\frac{1}{2} (x^{2} - 6 x + 5))

ln (x^{2} - 6 x + 5) - ln (2)

Solution steps

ln (\frac{1}{2} (x^{2} - 6 x + 5))

Apply log rule:

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

ln (\frac{1}{2} (x^{2} - 6 x + 5)) = ln (\frac{1}{2}) + ln (x^{2} - 6 x + 5)

= ln (\frac{1}{2}) + ln (x^{2} - 6 x + 5)

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} - 6 x + 5)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (2) + ln (x^{2} - 6 x + 5)

0 - ln (2) + ln (x^{2} - 6 x + 5) = - ln (2) + ln (x^{2} - 6 x + 5)

= ln (x^{2} - 6 x + 5) - ln (2)

- ln ∣ 6.1 - 3 ∣ + 2 ln ∣ 6.1 - 2 ∣ + c

lo g_{2} (a) + \frac{1}{2} lo g_{2} (b) - 3 lo g_{2} (c)

- ln (4) + ln (5)

ln (6) + ln (9)

- 30000 ln (\frac{49}{50})

What is ln(1/2 (x^2-6x+5)) ?
The solution to ln(1/2 (x^2-6x+5)) is ln(x^2-6x+5)-ln(2)