What is 8ln(3)-8ln(2) ?

The solution to 8ln(3)-8ln(2) is ln(6561/256)

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simplify 8ln(3)-8ln(2)

simplify

8 ln (3) - 8 ln (2)

ln (\frac{6561}{256})

Decimal Notation

3.24372 \dots

Solution steps

8 ln (3) - 8 ln (2)

Apply log rule:

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

8 ln (3) = ln (3^{8})

= ln (3^{8}) - 8 ln (2)

Apply log rule:

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

8 ln (2) = ln (2^{8})

= ln (3^{8}) - ln (2^{8})

Apply log rule:

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

ln (3^{8}) - ln (2^{8}) = ln (\frac{3 ^{8}}{2 ^{8}})

= ln (\frac{3 ^{8}}{2 ^{8}})

\frac{3 ^{8}}{2 ^{8}} = \frac{6561}{256}

= ln (\frac{6561}{256})

lo g_{e} (\frac{9}{4})

- lo g_{10} (8.07 \cdot 1 0^{- 7})

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