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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

ln (\frac{1643.85}{547.85}) \cdot 10

\frac{1}{2} ln (\frac{u - a}{u + a})

ln (\frac{3 x}{7})

ln (2 (3)^{x})

ln (\frac{1}{\frac{x c d}{d x}})

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