What is ln(x)-2[ln(x-7)+ln(x+7)] ?

The solution to ln(x)-2[ln(x-7)+ln(x+7)] is ln(x)-2ln((x-7)(x+7))

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simplify ln(x)-2[ln(x-7)+ln(x+7)]

simplify

ln (x) - 2 [ln (x - 7) + ln (x + 7)]

ln (x) - 2 ln ((x - 7) (x + 7))

Solution steps

ln (x) - 2 [ln (x - 7) + ln (x + 7)]

Apply log rule:

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

ln (x - 7) + ln (x + 7) = ln ((x - 7) (x + 7))

= ln (x) - 2 [ln ((x - 7) (x + 7))]

Remove parentheses:

(a) = a

= ln (x) - 2 ln ((x - 7) (x + 7))

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

lo g_{a} (\frac{3 ^{4}}{4 ^{2} a ^{7}})

ln (x^{\frac{1}{2}} y^{9}) - ln (z^{4})

ln (x) + ln (y) - 5 ln (z)

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

What is ln(x)-2[ln(x-7)+ln(x+7)] ?
The solution to ln(x)-2[ln(x-7)+ln(x+7)] is ln(x)-2ln((x-7)(x+7))