What is 1/3 [5ln(x+6)-ln(x)-ln(x^2-25)] ?

The solution to 1/3 [5ln(x+6)-ln(x)-ln(x^2-25)] is 1/3 ln(((x+6)^5)/(x(x^2-25)))

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simplify 1/3 [5ln(x+6)-ln(x)-ln(x^2-25)]

simplify

\frac{1}{3} [5 ln (x + 6) - ln (x) - ln (x^{2} - 25)]

\frac{1}{3} ln (\frac{( x + 6 ) ^{5}}{x ( x ^{2} - 25 )})

Solution steps

\frac{1}{3} [5 ln (x + 6) - ln (x) - ln (x^{2} - 25)]

Apply log rule:

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

5 ln (x + 6) = ln ((x + 6)^{5})

= \frac{1}{3} [ln ((x + 6)^{5}) - ln (x) - ln (x^{2} - 25)]

Apply log rule:

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

ln ((x + 6)^{5}) - ln (x) = ln (\frac{( x + 6 ) ^{5}}{x})

= \frac{1}{3} [ln (\frac{( x + 6 ) ^{5}}{x}) - ln (x^{2} - 25)]

Apply log rule:

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

ln (\frac{( x + 6 ) ^{5}}{x}) - ln (x^{2} - 25) = ln (\frac{\frac{( x + 6 ) ^{5}}{x}}{x ^{2} - 25})

= \frac{1}{3} [ln (\frac{\frac{( x + 6 ) ^{5}}{x}}{x ^{2} - 25})]

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{1}{3} [ln (\frac{( x + 6 ) ^{5}}{x ( x ^{2} - 25 )})]

Remove parentheses:

(a) = a

= \frac{1}{3} ln (\frac{( x + 6 ) ^{5}}{x ( x ^{2} - 25 )})

ln (\frac{x}{x - 1})

ln (\frac{e x ^{8}}{y})

lo g_{6} (36 x^{7})

lo g_{3} (a) + lo g_{3} (a + 6)

lo g_{3} (a) + lo g_{3} (a + 9)

What is 1/3 [5ln(x+6)-ln(x)-ln(x^2-25)] ?
The solution to 1/3 [5ln(x+6)-ln(x)-ln(x^2-25)] is 1/3 ln(((x+6)^5)/(x(x^2-25)))