What is ln(x^7-1)-ln(x^5-1) ?

The solution to ln(x^7-1)-ln(x^5-1) is ln((x^6+x^5+x^4+x^3+x^2+x+1)/(x^4+x^3+x^2+x+1))

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simplify ln(x^7-1)-ln(x^5-1)

simplify

ln (x^{7} - 1) - ln (x^{5} - 1)

ln (\frac{x ^{6} + x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{4} + x ^{3} + x ^{2} + x + 1})

Solution steps

ln (x^{7} - 1) - ln (x^{5} - 1)

Apply log rule:

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

ln (x^{7} - 1) - ln (x^{5} - 1) = ln (\frac{x ^{7} - 1}{x ^{5} - 1})

= ln (\frac{x ^{7} - 1}{x ^{5} - 1})

Simplify

\frac{x ^{7} - 1}{x ^{5} - 1} : \frac{x ^{6} + x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{4} + x ^{3} + x ^{2} + x + 1}

= ln (\frac{x ^{6} + x ^{5} + x ^{4} + x ^{3} + x ^{2} + x + 1}{x ^{4} + x ^{3} + x ^{2} + x + 1})

lo g_{3} (\frac{27 b ^{3} y ^{2} - 1}{y ( x + 1 ) ^{2}})

\frac{1}{20} ln (2)

\frac{1}{2} ln (\frac{25}{22})

ln (3 x) + ln (x^{4})

What is ln(x^7-1)-ln(x^5-1) ?
The solution to ln(x^7-1)-ln(x^5-1) is ln((x^6+x^5+x^4+x^3+x^2+x+1)/(x^4+x^3+x^2+x+1))