What is 1/3-3/2+9+27ln(4)-27ln(3) ?

The solution to 1/3-3/2+9+27ln(4)-27ln(3) is 27ln(4/3)+47/6

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simplify 1/3-3/2+9+27ln(4)-27ln(3)

simplify

\frac{1}{3} - \frac{3}{2} + 9 + 27 ln (4) - 27 ln (3)

27 ln (\frac{4}{3}) + \frac{47}{6}

Decimal Notation

15.60074 \dots

Solution steps

\frac{1}{3} - \frac{3}{2} + 9 + 27 ln (4) - 27 ln (3)

Apply log rule:

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

27 ln (4) = ln (4^{27})

= \frac{1}{3} - \frac{3}{2} + 9 + ln (4^{27}) - 27 ln (3)

Apply log rule:

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

27 ln (3) = ln (3^{27})

= \frac{1}{3} - \frac{3}{2} + 9 + ln (4^{27}) - ln (3^{27})

Apply log rule:

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

ln (4^{27}) - ln (3^{27}) = ln (\frac{4 ^{27}}{3 ^{27}})

= \frac{1}{3} - \frac{3}{2} + 9 + ln (\frac{4 ^{27}}{3 ^{27}})

ln (\frac{4 ^{27}}{3 ^{27}}) = 27 ln (\frac{4}{3})

= \frac{1}{3} - \frac{3}{2} + 9 + 27 ln (\frac{4}{3})

Combine the fractions

9 + \frac{1}{3} - \frac{3}{2} : \frac{47}{6}

= 27 ln (\frac{4}{3}) + \frac{47}{6}

- \frac{364}{1740} - 1.144 - ln (1.10066) + 0.5 ln (2)

\frac{1}{2} \cdot ln (\frac{29}{5})

ln (\frac{2}{9}) - 4

ln (\frac{7.2 x}{1.66})

ln (49) - ln (9) - ln (4)

What is 1/3-3/2+9+27ln(4)-27ln(3) ?
The solution to 1/3-3/2+9+27ln(4)-27ln(3) is 27ln(4/3)+47/6