What is ln|u^2-3u+1|+2ln|y| ?

The solution to ln|u^2-3u+1|+2ln|y| is ln(y^2|u^2-3u+1|)

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simplify ln|u^2-3u+1|+2ln|y|

simplify

ln u^{2} - 3 u + 1 + 2 ln ∣ y ∣

ln (y^{2} u^{2} - 3 u + 1)

Solution steps

ln u^{2} - 3 u + 1 + 2 ln ∣ y ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln ∣ y ∣ = ln (∣ y ∣^{2})

= ln u^{2} - 3 u + 1 + ln (∣ y ∣^{2})

Apply log rule:

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

ln u^{2} - 3 u + 1 + ln (∣ y ∣^{2}) = ln (∣ y ∣^{2} u^{2} - 3 u + 1)

= ln (∣ y ∣^{2} u^{2} - 3 u + 1)

∣ y ∣^{2} = y^{2}

= ln (y^{2} u^{2} - 3 u + 1)

(2 + 2 ln (2) + \frac{1}{2} + ln (3)) - (1 - 2 ln (1) + 1 + ln (2))

lo g_{2} (\frac{4 x ^{3}}{x ^{2} - 3 x - 18})

ln (6) + ln (\frac{e ^{(2.48199)}}{3})

(ln (100) - ln (95)) \cdot 100

What is ln|u^2-3u+1|+2ln|y| ?
The solution to ln|u^2-3u+1|+2ln|y| is ln(y^2|u^2-3u+1|)