What is ln(x-4)[ln(x+3)+ln(x-5)] ?

The solution to ln(x-4)[ln(x+3)+ln(x-5)] is ln(x-4)ln((x+3)(x-5))

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simplify ln(x-4)[ln(x+3)+ln(x-5)]

simplify

ln (x - 4) [ln (x + 3) + ln (x - 5)]

ln (x - 4) ln ((x + 3) (x - 5))

Solution steps

ln (x - 4) [ln (x + 3) + ln (x - 5)]

Apply log rule:

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

ln (x + 3) + ln (x - 5) = ln ((x + 3) (x - 5))

= ln (x - 4) [ln ((x + 3) (x - 5))]

Remove parentheses:

(a) = a

= ln (x - 4) ln ((x + 3) (x - 5))

\frac{1}{2} ln (x + 1) + \frac{1}{2} ln (x - 1)

\frac{1}{4} ln (\frac{3 tan ( \frac{x}{2} + 1 )}{tan ( \frac{x}{2} + 3 )}) + c

3 (ln (6) - ln (3))

\frac{1}{6} lo g_{2} (\frac{1}{6}) - \frac{5}{6} lo g_{2} (\frac{5}{6})

ln (x) - ln (- x + 1)

What is ln(x-4)[ln(x+3)+ln(x-5)] ?
The solution to ln(x-4)[ln(x+3)+ln(x-5)] is ln(x-4)ln((x+3)(x-5))