write as the sum and/or difference of logarithms. Express powers as factors.

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write as the sum and/or difference of logarithms. Express powers as factors.

Mathematics
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\[\log_{6} \left( x-4/x^7 \right)\]
first combine the inside into one fraction with x^7 as common denominator x - 4/x^7 = (x^8 - 4)/x^7 Now that we have division we split it into 2 logs using the log rule: logx - logy = log(x/y) *note the base does not change =>log(x^8 - 4) - log(x^7) Another rule is log(x^n) = n*log(x) so change log(x^7) to 7log(x) => log(x^8 -4) - 7log(x) Now we can factor x^8 -4 into a squared binomial: (x^4+2)(x^4-2) =>log((x^4+2)*(x^4-2)) - 7log(x) Now we have multiplication in our log so we split that into 2 logs logx + logy = logxy =>log(x^4+2) + log(x^4-2) - 7log(x) ok now i hope you get the idea, these could be factored again and split up and so on

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