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Popular >

simplify 1/3 ln(1/27)

Solution

simplify

\frac{1}{3} ln (\frac{1}{27})

Solution

- ln (3)

+1

Decimal Notation

- 1.09861 \dots

Solution steps

\frac{1}{3} ln (\frac{1}{27})

Apply log rule:

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

ln (\frac{1}{27}) = ln (1) - ln (27)

= \frac{1}{3} (ln (1) - ln (27))

Apply log rule:

lo g_{a} (1) = 0

= \frac{1}{3} (- ln (27) + 0)

0 - ln (27) = - ln (27)

= \frac{1}{3} (- ln (27))

Remove parentheses:

(- a) = - a

= - \frac{1}{3} ln (27)

Simplify

ln (27) : 3 ln (3)

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

3

= - ln (3) \cdot 1

Multiply:

ln (3) \cdot 1 = ln (3)

= - ln (3)

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Frequently Asked Questions (FAQ)

What is 1/3 ln(1/27) ?
The solution to 1/3 ln(1/27) is -ln(3)