What is ln(x)-3[4ln(x-6)-ln(x+6)] ?

The solution to ln(x)-3[4ln(x-6)-ln(x+6)] is ln(x)-3ln(((x-6)^4)/(x+6))

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simplify ln(x)-3[4ln(x-6)-ln(x+6)]

simplify

ln (x) - 3 [4 ln (x - 6) - ln (x + 6)]

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

Solution steps

ln (x) - 3 [4 ln (x - 6) - ln (x + 6)]

Apply log rule:

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

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

= ln (x) - 3 [ln ((x - 6)^{4}) - ln (x + 6)]

Apply log rule:

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

ln ((x - 6)^{4}) - ln (x + 6) = ln (\frac{( x - 6 ) ^{4}}{x + 6})

= ln (x) - 3 [ln (\frac{( x - 6 ) ^{4}}{x + 6})]

Remove parentheses:

(a) = a

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

ln (7 x)

lo g_{4} (9 x y)

3 - 3 lo g_{6} (2) - lo g_{6} (9)

ln (x^{8} 5 - x)

What is ln(x)-3[4ln(x-6)-ln(x+6)] ?
The solution to ln(x)-3[4ln(x-6)-ln(x+6)] is ln(x)-3ln(((x-6)^4)/(x+6))