What is 1/3 (3ln(x+4)+ln(x)-ln(x^2-5)) ?

The solution to 1/3 (3ln(x+4)+ln(x)-ln(x^2-5)) is 1/3 ln(((x+4)^3x)/(x^2-5))

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simplify 1/3 (3ln(x+4)+ln(x)-ln(x^2-5))

simplify

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 5))

\frac{1}{3} ln (\frac{( x + 4 ) ^{3} x}{x ^{2} - 5})

Solution steps

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 5))

Apply log rule:

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

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

= \frac{1}{3} (ln ((x + 4)^{3}) + ln (x) - ln (x^{2} - 5))

Apply log rule:

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

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

= \frac{1}{3} (ln ((x + 4)^{3} x) - ln (x^{2} - 5))

Apply log rule:

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

ln (x (x + 4)^{3}) - ln (x^{2} - 5) = ln (\frac{x ( x + 4 ) ^{3}}{x ^{2} - 5})

= \frac{1}{3} ln (\frac{( x + 4 ) ^{3} x}{x ^{2} - 5})

2 lo g_{x} (- 3 lo g_{y} (+ 4 lo g_{z} (x)))

lo g_{10} (\frac{y ^{5}}{z ^{2} x ^{3}})

4 ln (x) + 2 ln (y)

4 lo g_{b} (q) - lo g_{b} (r)

ln (x x^{2} - 8)

What is 1/3 (3ln(x+4)+ln(x)-ln(x^2-5)) ?
The solution to 1/3 (3ln(x+4)+ln(x)-ln(x^2-5)) is 1/3 ln(((x+4)^3x)/(x^2-5))