What is simplify-ln(x-2)-ln((x+1)^2) ?

The solution to simplify-ln(x-2)-ln((x+1)^2) is -ln((x-2)(x+1)^2)

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simplify-ln(x-2)-ln((x+1)^2)

simplify

- ln (x - 2) - ln ((x + 1)^{2})

- ln ((x - 2) (x + 1)^{2})

Solution steps

- ln (x - 2) - ln ((x + 1)^{2})

Rewrite

- ln (x - 2) - ln ((x + 1)^{2})

- (ln (x - 2) + ln ((x + 1)^{2}))

= - (ln (x - 2) + ln ((x + 1)^{2}))

Apply log rule:

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

ln (x - 2) + ln ((x + 1)^{2}) = ln ((x + 1)^{2} (x - 2))

= - ln ((x - 2) (x + 1)^{2})

ln ((1) (3))

2 ln (3) + 2 ln (4)

ln (11) - ln (6)

2 ln (6) - 2 ln (4)

ln (22 x)

What is simplify-ln(x-2)-ln((x+1)^2) ?
The solution to simplify-ln(x-2)-ln((x+1)^2) is -ln((x-2)(x+1)^2)