What is 1/3 (3ln(x+4)+ln(x)-ln(x^2-8)) ?

The solution to 1/3 (3ln(x+4)+ln(x)-ln(x^2-8)) is 1/3 ln(((x+4)^3x)/(x^2-8))

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simplify 1/3 (3ln(x+4)+ln(x)-ln(x^2-8))

simplify

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 8))

\frac{1}{3} ln (\frac{( x + 4 ) ^{3} x}{x ^{2} - 8})

Solution steps

\frac{1}{3} (3 ln (x + 4) + ln (x) - ln (x^{2} - 8))

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} - 8))

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} - 8))

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} - 8) = ln (\frac{x ( x + 4 ) ^{3}}{x ^{2} - 8})

= \frac{1}{3} ln (\frac{( x + 4 ) ^{3} x}{x ^{2} - 8})

6 ln (\frac{a}{5}) + 4 ln (7 b)

8 \cdot lo g_{b} (x) + 9 \cdot lo g_{b} (y) - 4 \cdot lo g_{b} (z)

ln (1 i)

ln (- 2 t)

\frac{ln ( 3.4 ) - ln ( 1.2 )}{0.01 ln ( 2 )}

What is 1/3 (3ln(x+4)+ln(x)-ln(x^2-8)) ?
The solution to 1/3 (3ln(x+4)+ln(x)-ln(x^2-8)) is 1/3 ln(((x+4)^3x)/(x^2-8))