What is 9/2 ln(3/2)+3/8-ln(2)-ln(2) ?

The solution to 9/2 ln(3/2)+3/8-ln(2)-ln(2) is ln((81sqrt(6))/(128))+3/8

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simplify 9/2 ln(3/2)+3/8-ln(2)-ln(2)

simplify

\frac{9}{2} ln (\frac{3}{2}) + \frac{3}{8} - ln (2) - ln (2)

ln (\frac{81 6}{128}) + \frac{3}{8}

Decimal Notation

0.81329 \dots

Solution steps

\frac{9}{2} ln (\frac{3}{2}) + \frac{3}{8} - ln (2) - ln (2)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln ((\frac{3}{2})^{\frac{9}{2}}) + \frac{3}{8} - ln (2) - ln (2)

Apply log rule:

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

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

= ln \frac{( \frac{3}{2} ) ^{\frac{9}{2}}}{2} + \frac{3}{8} - ln (2)

\frac{( \frac{3}{2} ) ^{\frac{9}{2}}}{2} = \frac{81 6}{64}

= ln (\frac{81 6}{64}) + \frac{3}{8} - ln (2)

Apply log rule:

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

ln (\frac{81 6}{64}) - ln (2) = ln (\frac{\frac{81 6}{64}}{2})

= ln (\frac{\frac{81 6}{64}}{2}) + \frac{3}{8}

\frac{\frac{81 6}{64}}{2} = \frac{81 6}{128}

= ln (\frac{81 6}{128}) + \frac{3}{8}

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What is 9/2 ln(3/2)+3/8-ln(2)-ln(2) ?
The solution to 9/2 ln(3/2)+3/8-ln(2)-ln(2) is ln((81sqrt(6))/(128))+3/8