What is 7/2-9ln(4)+9ln(3) ?

The solution to 7/2-9ln(4)+9ln(3) is 7/2+ln(19683/262144)

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simplify 7/2-9ln(4)+9ln(3)

simplify

\frac{7}{2} - 9 ln (4) + 9 ln (3)

\frac{7}{2} + ln (\frac{19683}{262144})

Decimal Notation

0.91086 \dots

Solution steps

\frac{7}{2} - 9 ln (4) + 9 ln (3)

Apply log rule:

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

9 ln (4) = ln (4^{9})

= \frac{7}{2} - ln (4^{9}) + 9 ln (3)

Apply log rule:

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

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

= \frac{7}{2} - ln (4^{9}) + ln (3^{9})

Apply log rule:

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

ln (3^{9}) - ln (4^{9}) = ln (\frac{3 ^{9}}{4 ^{9}})

= \frac{7}{2} + ln (\frac{3 ^{9}}{4 ^{9}})

\frac{3 ^{9}}{4 ^{9}} = \frac{19683}{262144}

= \frac{7}{2} + ln (\frac{19683}{262144})

ln (x) + ln (4 x)

ln (3 a) - ln (2 b)

5 lo g_{3} (q) + 2 lo g_{3} (y)

ln (\frac{z}{x - y})

\frac{1}{3} ln (\frac{47}{56.37})

What is 7/2-9ln(4)+9ln(3) ?
The solution to 7/2-9ln(4)+9ln(3) is 7/2+ln(19683/262144)