What is 2[3ln(x)-ln(x+6)-ln(x-6)] ?

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

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simplify 2[3ln(x)-ln(x+6)-ln(x-6)]

simplify

2 [3 ln (x) - ln (x + 6) - ln (x - 6)]

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

Solution steps

2 [3 ln (x) - ln (x + 6) - ln (x - 6)]

Apply log rule:

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

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

= 2 [ln (x^{3}) - ln (x + 6) - ln (x - 6)]

Apply log rule:

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

ln (x^{3}) - ln (x + 6) = ln (\frac{x ^{3}}{x + 6})

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

Apply log rule:

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

ln (\frac{x ^{3}}{x + 6}) - ln (x - 6) = ln (\frac{\frac{x ^{3}}{x + 6}}{x - 6})

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

Apply the fraction rule:

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

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

Remove parentheses:

(a) = a

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

lo g_{10} (\frac{t}{11})

ln (\frac{x}{10})

ln (\frac{tan ( θ ) + sec ( θ )}{tan ( \frac{θ}{2} )})

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

lo g_{4} (\frac{6 x ^{2}}{5 y ^{3}})

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