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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (x - 2) + ln (x + 2) = ln ((x - 2) (x + 2))

= ln (x) - 4 ln ((x - 2) (x + 2))

Apply log rule:

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

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

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

Apply log rule:

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

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

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

((x - 2) (x + 2))^{4} = (x - 2)^{4} (x + 2)^{4}

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

ln (5 \cdot 1 0^{4})

- ln \frac{v}{v - c} + ln \frac{v}{v + c}

ln (x^{2} - 2 x) - ln (3)

ln (4 x y)

ln (\frac{373}{283})

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