What is ln(4(x^2-4x+6)^3) ?

The solution to ln(4(x^2-4x+6)^3) is 2ln(2)+3ln(x^2-4x+6)

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simplify ln(4(x^2-4x+6)^3)

simplify

ln (4 (x^{2} - 4 x + 6)^{3})

2 ln (2) + 3 ln (x^{2} - 4 x + 6)

Solution steps

ln (4 (x^{2} - 4 x + 6)^{3})

Apply log rule:

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

ln (4 (x^{2} - 4 x + 6)^{3}) = ln (4) + ln ((x^{2} - 4 x + 6)^{3})

= ln (4) + ln ((x^{2} - 4 x + 6)^{3})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((x^{2} - 4 x + 6)^{3}) = 3 ln (x^{2} - 4 x + 6)

= ln (4) + 3 ln (x^{2} - 4 x + 6)

ln (4) = 2 ln (2)

= 2 ln (2) + 3 ln (x^{2} - 4 x + 6)

3 ln (x + 5) - 8 ln (x)

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

ln (\frac{x}{41})

ln (\frac{x}{x - 3})

- lo g_{10} (8.8 \cdot 1 0^{- 3})

What is ln(4(x^2-4x+6)^3) ?
The solution to ln(4(x^2-4x+6)^3) is 2ln(2)+3ln(x^2-4x+6)