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

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

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

simplify

ln (x + 2) + ln (x - 2) - 3 ln (x)

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

Solution steps

ln (x + 2) + ln (x - 2) - 3 ln (x)

Apply log rule:

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

ln (x + 2) + ln (x - 2) = ln ((x + 2) (x - 2))

= ln ((x + 2) (x - 2)) - 3 ln (x)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

ln (x) - 3 ln (z) + 12 ln (y)

2 ln (\frac{5 e}{3})

4 ln (x y) + ln (y) - ln (x^{4} y)

2 ln (5) + 3 ln (4)

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