What is 7ln(x)-ln(x^2-4)+ln(x^2+2x) ?

The solution to 7ln(x)-ln(x^2-4)+ln(x^2+2x) is ln((x^8)/(x-2))

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simplify 7ln(x)-ln(x^2-4)+ln(x^2+2x)

simplify

7 ln (x) - ln (x^{2} - 4) + ln (x^{2} + 2 x)

ln (\frac{x ^{8}}{x - 2})

Solution steps

7 ln (x) - ln (x^{2} - 4) + ln (x^{2} + 2 x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

7 ln (x) = ln (x^{7})

= ln (x^{7}) - ln (x^{2} - 4) + ln (x^{2} + 2 x)

Apply log rule:

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

ln (x^{7}) - ln (x^{2} - 4) = ln (\frac{x ^{7}}{x ^{2} - 4})

= ln (\frac{x ^{7}}{x ^{2} - 4}) + ln (x^{2} + 2 x)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{x ^{7}}{x ^{2} - 4}) + ln (x^{2} + 2 x) = ln (\frac{x ^{7}}{x ^{2} - 4} (x^{2} + 2 x))

= ln (\frac{x ^{7}}{x ^{2} - 4} (x^{2} + 2 x))

Simplify

\frac{x ^{7}}{x ^{2} - 4} (x^{2} + 2 x) : \frac{x ^{8}}{x - 2}

= ln (\frac{x ^{8}}{x - 2})

lo g_{10} (y) + 7 lo g_{10} (z)

lo g_{4} (x^{2} - 49) - 4 lo g_{4} (x + 7)

f (x) = lo g_{7} (x) - lo g_{7} (x^{7})

f (x) = lo g_{7} (x + 1) + 2 lo g_{7} (x + 4) - 3 lo g_{7} (x - 5)

lo g_{10} (4) - 1 + lo g_{10} (\frac{1}{2})

What is 7ln(x)-ln(x^2-4)+ln(x^2+2x) ?
The solution to 7ln(x)-ln(x^2-4)+ln(x^2+2x) is ln((x^8)/(x-2))