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Popular >

simplify 3ln(1/3)

Solution

simplify

3 ln (\frac{1}{3})

Solution

- 3 ln (3)

+1

Decimal Notation

- 3.29583 \dots

Solution steps

3 ln (\frac{1}{3})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{1}{3}) = ln (1) - ln (3)

= 3 (ln (1) - ln (3))

Apply log rule:

lo g_{a} (1) = 0

= 3 (- ln (3) + 0)

0 - ln (3) = - ln (3)

= 3 (- ln (3))

Remove parentheses:

(- a) = - a

= - 3 ln (3)

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Frequently Asked Questions (FAQ)

What is 3ln(1/3) ?
The solution to 3ln(1/3) is -3ln(3)