What is 9/2 ln(9/2) ?

The solution to 9/2 ln(9/2) is 9ln(3)-9/2 ln(2)

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simplify 9/2 ln(9/2)

simplify

\frac{9}{2} ln (\frac{9}{2})

9 ln (3) - \frac{9}{2} ln (2)

Decimal Notation

6.76834 \dots

Solution steps

\frac{9}{2} ln (\frac{9}{2})

Apply log rule:

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

ln (\frac{9}{2}) = ln (9) - ln (2)

= \frac{9}{2} (ln (9) - ln (2))

ln (9) = 2 ln (3)

= \frac{9}{2} (2 ln (3) - ln (2))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{9}{2}, b = 2 ln (3), c = ln (2)

= \frac{9}{2} \cdot 2 ln (3) - \frac{9}{2} ln (2)

= 2 \cdot \frac{9}{2} ln (3) - \frac{9}{2} ln (2)

2 \cdot \frac{9}{2} ln (3) = 9 ln (3)

= 9 ln (3) - \frac{9}{2} ln (2)

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