What is (6ln(3)-10ln(2))/2 ?

The solution to (6ln(3)-10ln(2))/2 is (ln(729/1024))/2

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simplify (6ln(3)-10ln(2))/2

simplify

\frac{6 ln ( 3 ) - 10 ln ( 2 )}{2}

\frac{ln ( \frac{729}{1024} )}{2}

Decimal Notation

- 0.16989 \dots

Solution steps

\frac{6 ln ( 3 ) - 10 ln ( 2 )}{2}

Apply log rule:

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

6 ln (3) = ln (3^{6})

= \frac{ln ( 3 ^{6} ) - 10 ln ( 2 )}{2}

Apply log rule:

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

10 ln (2) = ln (2^{10})

= \frac{ln ( 3 ^{6} ) - ln ( 2 ^{10} )}{2}

Apply log rule:

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

ln (3^{6}) - ln (2^{10}) = ln (\frac{3 ^{6}}{2 ^{10}})

= \frac{ln ( \frac{3 ^{6}}{2 ^{10}} )}{2}

\frac{3 ^{6}}{2 ^{10}} = \frac{729}{1024}

= \frac{ln ( \frac{729}{1024} )}{2}

\frac{1}{2} ln (\frac{2}{2})

ln (\frac{7 x ^{5}}{y ^{3}})

ln (9616) - 2 ln (96)

4 ln (x) + 6 ln (y) + 3 ln (z)

5 lo g_{2} (x) + 7 lo g_{2} (y)

What is (6ln(3)-10ln(2))/2 ?
The solution to (6ln(3)-10ln(2))/2 is (ln(729/1024))/2