What is 2[(ln(x+3)+ln(x)-ln(x^2-1))] ?

The solution to 2[(ln(x+3)+ln(x)-ln(x^2-1))] is 2ln((x(x+3))/(x^2-1))

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simplify 2[(ln(x+3)+ln(x)-ln(x^2-1))]

simplify

2 [(ln (x + 3) + ln (x) - ln (x^{2} - 1))]

2 ln (\frac{x ( x + 3 )}{x ^{2} - 1})

Solution steps

2 [(ln (x + 3) + ln (x) - ln (x^{2} - 1))]

Apply log rule:

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

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

= 2 [ln ((x + 3) x) - ln (x^{2} - 1)]

Apply log rule:

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

ln (x (x + 3)) - ln (x^{2} - 1) = ln (\frac{x ( x + 3 )}{x ^{2} - 1})

= 2 [ln (\frac{( x + 3 ) x}{x ^{2} - 1})]

Remove parentheses:

(a) = a

= 2 ln (\frac{( x + 3 ) x}{x ^{2} - 1})

ln (\frac{x ^{2}}{y ^{3} z ^{4}})

ln \frac{3}{2} - ln \frac{1}{2}

lo g_{4} (\frac{1}{44})

e^{x y} + ln (y) + ln (x)

What is 2[(ln(x+3)+ln(x)-ln(x^2-1))] ?
The solution to 2[(ln(x+3)+ln(x)-ln(x^2-1))] is 2ln((x(x+3))/(x^2-1))