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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

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

Apply the fraction rule:

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

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

Remove parentheses:

(a) = a

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

- lo g_{10} (\frac{x}{y})

lo g_{10} (x^{3} y)

lo g_{10} (a) + 9 lo g_{10} (b)

ln (x^{15} 2 - x)

ln (\frac{5 ^{2}}{5 ^{2} + ( - 5 ) ^{2}})

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