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})

3 lo g_{10} (x + 1) + lo g_{10} (y) - 2 lo g_{10} (x)

2 lo g_{10} (x) - lo g_{10} (\frac{1}{x}) - lo g_{10} (y)

lo g_{10} (\frac{2 x ^{3} + 4}{5 x ^{3} - x})

33.33 (1) ln (\frac{1100}{1400}) - 0.287 ln (\frac{5}{20})

ln (7) + 2 ln (5)

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))