What is 1/3 (6ln(x+4)+ln(x)-ln(x^2-8)) ?

The solution to 1/3 (6ln(x+4)+ln(x)-ln(x^2-8)) is 1/3 ln(((x+4)^6x)/(x^2-8))

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simplify 1/3 (6ln(x+4)+ln(x)-ln(x^2-8))

simplify

\frac{1}{3} (6 ln (x + 4) + ln (x) - ln (x^{2} - 8))

\frac{1}{3} ln (\frac{( x + 4 ) ^{6} x}{x ^{2} - 8})

Solution steps

\frac{1}{3} (6 ln (x + 4) + ln (x) - ln (x^{2} - 8))

Apply log rule:

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

6 ln (x + 4) = ln ((x + 4)^{6})

= \frac{1}{3} (ln ((x + 4)^{6}) + ln (x) - ln (x^{2} - 8))

Apply log rule:

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

ln ((x + 4)^{6}) + ln (x) = ln (x (x + 4)^{6})

= \frac{1}{3} (ln ((x + 4)^{6} 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)^{6}) - ln (x^{2} - 8) = ln (\frac{x ( x + 4 ) ^{6}}{x ^{2} - 8})

= \frac{1}{3} ln (\frac{( x + 4 ) ^{6} x}{x ^{2} - 8})

\frac{ln ( \frac{3}{2} )}{8 ln ( 10 )}

lo g_{2} (x^{2}) - lo g_{2} (x)

ln (\frac{k + 1}{k})

2 lo g_{10} (4 x) - lo g_{10} (8)

What is 1/3 (6ln(x+4)+ln(x)-ln(x^2-8)) ?
The solution to 1/3 (6ln(x+4)+ln(x)-ln(x^2-8)) is 1/3 ln(((x+4)^6x)/(x^2-8))