What is 30log_{6}(3)+30log_{6}(2)-6log_{6}(11) ?

The solution to 30log_{6}(3)+30log_{6}(2)-6log_{6}(11) is 30log_{6}(3)+log_{6}((2^{30})/(1771561))

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simplify 30log_{6}(3)+30log_{6}(2)-6log_{6}(11)

simplify

30 lo g_{6} (3) + 30 lo g_{6} (2) - 6 lo g_{6} (11)

30 lo g_{6} (3) + lo g_{6} (\frac{2 ^{30}}{1771561})

Decimal Notation

21.97025 \dots

Solution steps

30 lo g_{6} (3) + 30 lo g_{6} (2) - 6 lo g_{6} (11)

Apply log rule:

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

30 lo g_{6} (2) = lo g_{6} (2^{30})

= 30 lo g_{6} (3) + lo g_{6} (2^{30}) - 6 lo g_{6} (11)

Apply log rule:

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

6 lo g_{6} (11) = lo g_{6} (1 1^{6})

= 30 lo g_{6} (3) + lo g_{6} (2^{30}) - lo g_{6} (1 1^{6})

Apply log rule:

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

lo g_{6} (2^{30}) - lo g_{6} (1 1^{6}) = lo g_{6} (\frac{2 ^{30}}{1 1 ^{6}})

= 30 lo g_{6} (3) + lo g_{6} (\frac{2 ^{30}}{1 1 ^{6}})

1 1^{6} = 1771561

= 30 lo g_{6} (3) + lo g_{6} (\frac{2 ^{30}}{1771561})

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What is 30log_{6}(3)+30log_{6}(2)-6log_{6}(11) ?
The solution to 30log_{6}(3)+30log_{6}(2)-6log_{6}(11) is 30log_{6}(3)+log_{6}((2^{30})/(1771561))