What is ln(x^2-9)-ln(x+3)+3ln(x) ?

The solution to ln(x^2-9)-ln(x+3)+3ln(x) is ln((x-3)x^3)

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simplify ln(x^2-9)-ln(x+3)+3ln(x)

simplify

ln (x^{2} - 9) - ln (x + 3) + 3 ln (x)

ln ((x - 3) x^{3})

Solution steps

ln (x^{2} - 9) - ln (x + 3) + 3 ln (x)

Apply log rule:

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

ln (x^{2} - 9) - ln (x + 3) = ln (\frac{x ^{2} - 9}{x + 3})

= ln (\frac{x ^{2} - 9}{x + 3}) + 3 ln (x)

Simplify

\frac{x ^{2} - 9}{x + 3} : x - 3

= ln (x - 3) + 3 ln (x)

Apply log rule:

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

3 ln (x) = ln (x^{3})

= ln (x - 3) + ln (x^{3})

Apply log rule:

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

ln (x - 3) + ln (x^{3}) = ln (x^{3} (x - 3))

= ln ((x - 3) x^{3})

3 lo g_{3} (x) - 2 lo g_{3} (y)

ln (\frac{8 x ^{2}}{3 y})

ln (3^{x - 2} (3^{x} - 10))

ln (ux)

ln (x^{3} y^{3})

What is ln(x^2-9)-ln(x+3)+3ln(x) ?
The solution to ln(x^2-9)-ln(x+3)+3ln(x) is ln((x-3)x^3)