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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

= ln (\frac{1}{6}) + 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}{6}) = ln (1) - ln (6)

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

Apply log rule:

lo g_{a} (1) = 0

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

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

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

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