What is ln(x^3+8)-ln(x+2)-2ln(x^2-2x+4) ?

The solution to ln(x^3+8)-ln(x+2)-2ln(x^2-2x+4) is -ln(x^2-2x+4)

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simplify ln(x^3+8)-ln(x+2)-2ln(x^2-2x+4)

simplify

ln (x^{3} + 8) - ln (x + 2) - 2 ln (x^{2} - 2 x + 4)

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

Solution steps

ln (x^{3} + 8) - ln (x + 2) - 2 ln (x^{2} - 2 x + 4)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{3} + 8) - ln (x + 2) = ln (\frac{x ^{3} + 8}{x + 2})

= ln (\frac{x ^{3} + 8}{x + 2}) - 2 ln (x^{2} - 2 x + 4)

Simplify

\frac{x ^{3} + 8}{x + 2} : x^{2} - 2 x + 4

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

Add similar elements:

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

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

ln (x + 2) - ln (5 x)

lo g_{2} (8 x^{5})

lo g_{b} (x) + lo g_{b} (y) - lo g_{b} (t)

ln ((x^{2} + 5)^{5} (1 - x^{4})^{4})

What is ln(x^3+8)-ln(x+2)-2ln(x^2-2x+4) ?
The solution to ln(x^3+8)-ln(x+2)-2ln(x^2-2x+4) is -ln(x^2-2x+4)