What is 2[2ln(x)-ln(x+4)-ln(x-4)] ?

The solution to 2[2ln(x)-ln(x+4)-ln(x-4)] is 2ln((x^2)/((x+4)(x-4)))

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simplify 2[2ln(x)-ln(x+4)-ln(x-4)]

simplify

2 [2 ln (x) - ln (x + 4) - ln (x - 4)]

2 ln (\frac{x ^{2}}{( x + 4 ) ( x - 4 )})

Solution steps

2 [2 ln (x) - ln (x + 4) - ln (x - 4)]

Apply log rule:

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

2 ln (x) = ln (x^{2})

= 2 [ln (x^{2}) - ln (x + 4) - ln (x - 4)]

Apply log rule:

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

ln (x^{2}) - ln (x + 4) = ln (\frac{x ^{2}}{x + 4})

= 2 [ln (\frac{x ^{2}}{x + 4}) - ln (x - 4)]

Apply log rule:

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

ln (\frac{x ^{2}}{x + 4}) - ln (x - 4) = ln (\frac{\frac{x ^{2}}{x + 4}}{x - 4})

= 2 [ln (\frac{\frac{x ^{2}}{x + 4}}{x - 4})]

Apply the fraction rule:

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

= 2 [ln (\frac{x ^{2}}{( x + 4 ) ( x - 4 )})]

Remove parentheses:

(a) = a

= 2 ln (\frac{x ^{2}}{( x + 4 ) ( x - 4 )})

3 lo g_{2} (x) - lo g_{2} (y)

- lo g_{10} (5.16 \cdot 1 0^{- 6})

- ln (x^{6}) - ln (y^{6})

- ln (5.8) + 2 ln (6.8) + c

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

What is 2[2ln(x)-ln(x+4)-ln(x-4)] ?
The solution to 2[2ln(x)-ln(x+4)-ln(x-4)] is 2ln((x^2)/((x+4)(x-4)))