What is pi^{81}(ln(11)-3ln(2)) ?

The solution to pi^{81}(ln(11)-3ln(2)) is pi^{81}ln(11/8)

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simplify pi^{81}(ln(11)-3ln(2))

simplify

π^{81} (ln (11) - 3 ln (2))

π^{81} ln (\frac{11}{8})

Decimal Notation

5.91815 E 39

Solution steps

π^{81} (ln (11) - 3 ln (2))

Apply log rule:

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

3 ln (2) = ln (2^{3})

= π^{81} (ln (11) - ln (2^{3}))

Apply log rule:

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

ln (11) - ln (2^{3}) = ln (\frac{11}{2 ^{3}})

= π^{81} ln (\frac{11}{2 ^{3}})

2^{3} = 8

= π^{81} ln (\frac{11}{8})

3 lo g_{10} (x) - lo g_{10} (2)

ln (4 x y^{2}) - 2 ln (x^{2} y)

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

lo g_{10} (x^{3})

ln (b e^{- x})

What is pi^{81}(ln(11)-3ln(2)) ?
The solution to pi^{81}(ln(11)-3ln(2)) is pi^{81}ln(11/8)