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

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

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

simplify

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

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

Solution steps

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

Remove parentheses:

(a) = a

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

ln (\frac{x ^{2} - 1}{x ^{3}})

3 lo g_{b} (x) + 2 lo g_{b} (y) - \frac{1}{2} lo g_{b} (z)

lo g_{10} (\frac{x ^{3} y}{z})

4 lo g_{10} (\frac{x}{5})

- lo g_{10} (6.5 \cdot 1 0^{- 5})

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