What is 2ln(x-2)+ln(3)-ln(x^2-4) ?

The solution to 2ln(x-2)+ln(3)-ln(x^2-4) is ln((3(x-2))/(x+2))

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simplify 2ln(x-2)+ln(3)-ln(x^2-4)

simplify

2 ln (x - 2) + ln (3) - ln (x^{2} - 4)

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

Solution steps

2 ln (x - 2) + ln (3) - ln (x^{2} - 4)

Apply log rule:

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

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

= ln ((x - 2)^{2}) + ln (3) - ln (x^{2} - 4)

Apply log rule:

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

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

= ln ((x - 2)^{2} \cdot 3) - ln (x^{2} - 4)

Apply log rule:

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

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

= ln (\frac{( x - 2 ) ^{2} \cdot 3}{x ^{2} - 4})

Simplify

\frac{( x - 2 ) ^{2} \cdot 3}{x ^{2} - 4} : \frac{3 ( x - 2 )}{x + 2}

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

\frac{ln ( \frac{8}{9} )}{2} + ln (\frac{4}{3}) - 1

ln (\frac{100}{5.7})

ln (y) - ln (2)

\frac{1}{ln ( ( ln ( n ) ) ^{l n (n)} )}

\frac{1}{2} ln ∣ 10.8 + 1 ∣ + 2 ln ∣ 10.8 - 1 ∣

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