What is 2ln(2)+(17ln(2)-9ln(3))/5 ?

The solution to 2ln(2)+(17ln(2)-9ln(3))/5 is 2ln(2)+(ln(131072/19683))/5

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simplify 2ln(2)+(17ln(2)-9ln(3))/5

simplify

2 ln (2) + \frac{17 ln ( 2 ) - 9 ln ( 3 )}{5}

2 ln (2) + \frac{ln ( \frac{131072}{19683} )}{5}

Decimal Notation

1.76549 \dots

Solution steps

2 ln (2) + \frac{17 ln ( 2 ) - 9 ln ( 3 )}{5}

Apply log rule:

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

17 ln (2) = ln (2^{17})

= 2 ln (2) + \frac{ln ( 2 ^{17} ) - 9 ln ( 3 )}{5}

Apply log rule:

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

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

= 2 ln (2) + \frac{ln ( 2 ^{17} ) - ln ( 3 ^{9} )}{5}

Apply log rule:

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

ln (2^{17}) - ln (3^{9}) = ln (\frac{2 ^{17}}{3 ^{9}})

= 2 ln (2) + \frac{ln ( \frac{2 ^{17}}{3 ^{9}} )}{5}

\frac{2 ^{17}}{3 ^{9}} = \frac{131072}{19683}

= 2 ln (2) + \frac{ln ( \frac{131072}{19683} )}{5}

ln (x) - ln (x^{3})

lo g_{2} (\frac{6 x ^{2}}{y z ^{3}})

ln (\frac{ln ( e - x )}{x})

9 ln (9 x)

2 lo g_{\frac{3}{2}} (3)

What is 2ln(2)+(17ln(2)-9ln(3))/5 ?
The solution to 2ln(2)+(17ln(2)-9ln(3))/5 is 2ln(2)+(ln(131072/19683))/5