What is simplify-5/4 ln(1/4) ?

The solution to simplify-5/4 ln(1/4) is 5/2 ln(2)

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simplify-5/4 ln(1/4)

simplify

- \frac{5}{4} ln (\frac{1}{4})

\frac{5}{2} ln (2)

Decimal Notation

1.73286 \dots

Solution steps

- \frac{5}{4} ln (\frac{1}{4})

Apply log rule:

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

ln (\frac{1}{4}) = ln (1) - ln (4)

= - \frac{5}{4} (ln (1) - ln (4))

Apply log rule:

lo g_{a} (1) = 0

= - \frac{5}{4} (- ln (4) + 0)

0 - ln (4) = - ln (4)

= - \frac{5}{4} (- ln (4))

Apply rule

- (- a) = a

= \frac{5}{4} ln (4)

Simplify

ln (4) : 2 ln (2)

= 2 \cdot \frac{5}{4} ln (2)

Multiply fractions:

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

= \frac{5 \cdot 2}{4} ln (2)

\frac{5 \cdot 2}{4} = \frac{5}{2}

= \frac{5}{2} ln (2)

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What is simplify-5/4 ln(1/4) ?
The solution to simplify-5/4 ln(1/4) is 5/2 ln(2)