What is [ln(x^5-1)-ln(x^3-1)] ?

The solution to [ln(x^5-1)-ln(x^3-1)] is ln((x^4+x^3+x^2+x+1)/(x^2+x+1))

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simplify [ln(x^5-1)-ln(x^3-1)]

simplify

[ln (x^{5} - 1) - ln (x^{3} - 1)]

ln (\frac{x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{2} + x + 1})

Solution steps

[ln (x^{5} - 1) - ln (x^{3} - 1)]

Apply log rule:

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

ln (x^{5} - 1) - ln (x^{3} - 1) = ln (\frac{x ^{5} - 1}{x ^{3} - 1})

= [ln (\frac{x ^{5} - 1}{x ^{3} - 1})]

Simplify

\frac{x ^{5} - 1}{x ^{3} - 1} : \frac{x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{2} + x + 1}

= [ln (\frac{x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{2} + x + 1})]

Remove parentheses:

(a) = a

= ln (\frac{x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{2} + x + 1})

- (\frac{4}{6}) lo g_{2} (\frac{4}{6}) - (\frac{2}{6}) lo g_{2} (\frac{2}{6})

ln (\frac{5}{1})

ln (x e^{- x y})

lo g_{18} (\frac{13 r}{s})

What is [ln(x^5-1)-ln(x^3-1)] ?
The solution to [ln(x^5-1)-ln(x^3-1)] is ln((x^4+x^3+x^2+x+1)/(x^2+x+1))