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})

lo g_{4} ((m^{2} n^{3})^{5})

ln (\frac{10}{1})

lo g_{10} (\frac{z ^{2} y}{x ^{2}})

lo g_{3} (12 x^{7})

lo g_{10} (4 \cdot 1 0^{- 5})

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))