What is (27ln(2)-9ln(3))/5 ?

The solution to (27ln(2)-9ln(3))/5 is (ln(134217728/19683))/5

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simplify (27ln(2)-9ln(3))/5

simplify

\frac{27 ln ( 2 ) - 9 ln ( 3 )}{5}

\frac{ln ( \frac{134217728}{19683} )}{5}

Decimal Notation

1.76549 \dots

Solution steps

\frac{27 ln ( 2 ) - 9 ln ( 3 )}{5}

Apply log rule:

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

27 ln (2) = ln (2^{27})

= \frac{ln ( 2 ^{27} ) - 9 ln ( 3 )}{5}

Apply log rule:

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

9 ln (3) = ln (3^{9})

= \frac{ln ( 2 ^{27} ) - ln ( 3 ^{9} )}{5}

Apply log rule:

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

ln (2^{27}) - ln (3^{9}) = ln (\frac{2 ^{27}}{3 ^{9}})

= \frac{ln ( \frac{2 ^{27}}{3 ^{9}} )}{5}

\frac{2 ^{27}}{3 ^{9}} = \frac{134217728}{19683}

= \frac{ln ( \frac{134217728}{19683} )}{5}

ln (\frac{( 1 )}{12})

4 lo g_{8} (u) - 2 lo g_{8} (v)

ln (\frac{115}{120})

lo g_{b} (x) - 2 lo g_{b} (y)

\frac{1}{2} ln (2 x + 5) - \frac{1}{3} ln (x + 3) + ln (C)

What is (27ln(2)-9ln(3))/5 ?
The solution to (27ln(2)-9ln(3))/5 is (ln(134217728/19683))/5