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

The solution to ln(1-x^7)-ln(1-x^5) 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(1-x^7)-ln(1-x^5)

simplify

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

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

Apply log rule:

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

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

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

Simplify

\frac{1 - x ^{7}}{1 - x ^{5}} : \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})

e^{5} + ln (16 x)

lo g_{10} (9.28) - lo g_{10} (5.8)

ln (2 \frac{π}{2})

ln (\frac{2 ^{4}}{3 ^{- 4} 5 ^{4}})

ln (3 y e^{y})

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