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

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

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simplify 1/3 (2ln(x+3)+ln(x)-ln(x^2-1))

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

lo g_{2} (x) - 5 lo g_{2} (y)

lo g_{5} (x + 12) + lo g_{5} (x - 12)

lo g_{2} (\frac{7 r ^{5}}{z ^{7}})

ln (\frac{1}{N !})

lo g_{x} (\frac{x ^{3} y}{n ^{7}})

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