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

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

Popular >

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

simplify

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

\frac{9}{2} + ln (\frac{19683}{262144})

Decimal Notation

1.91086 \dots

Solution steps

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

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

= \frac{9}{2} + ln (\frac{19683}{262144})

\frac{d ^{4}}{d x ^{4}} (e^{- 4 x}) + 6 ln (3 x^{5})

ln (y) - \frac{1}{2} ln (y - 1) - \frac{1}{2} ln (y + 1)

ln (\frac{\frac{1}{2}}{\frac{1}{4}})

- 2 ln ∣ l + d ∣ + ln ∣ d ∣ + ln ∣ 2 l + d ∣

lo g_{4} (x^{2} - 1) - 5 lo g_{4} (x - 1)

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