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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Remove parentheses:

(a) = a

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

ln (\frac{2}{27})

lo g_{2} (\frac{a ^{2} - 9}{5})

lo g_{10} (\frac{x}{1000})

7 lo g_{10} (c) + lo g_{10} (q)

ln (\frac{6}{e ^{5}})

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