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

The solution to 27/5 ln(2)-9/5 ln(3) is ln((32*2^{2/5}\sqrt[5]{3})/(3^2))

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

simplify

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

Decimal Notation

1.76549 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (e x^{4}) + 4

ln (\frac{5 x ^{6}}{11 y ^{7}})

[\frac{( 8.314 \cdot 293 )}{( 2 \cdot 96485 )}] \cdot ln (\frac{1}{0.05})

ln (2) + ln (- 2) + 1

ln (\frac{0.007}{1})

What is 27/5 ln(2)-9/5 ln(3) ?
The solution to 27/5 ln(2)-9/5 ln(3) is ln((32*2^{2/5}\sqrt[5]{3})/(3^2))