What is 4log_{2}(11)-6log_{2}(6) ?

The solution to 4log_{2}(11)-6log_{2}(6) is log_{2}(14641/729)-6

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simplify 4log_{2}(11)-6log_{2}(6)

simplify

4 lo g_{2} (11) - 6 lo g_{2} (6)

lo g_{2} (\frac{14641}{729}) - 6

Decimal Notation

- 1.67204 \dots

Solution steps

4 lo g_{2} (11) - 6 lo g_{2} (6)

6 lo g_{2} (6) = 6 + 6 lo g_{2} (3)

= 4 lo g_{2} (11) - (6 + 6 lo g_{2} (3))

Apply the distributive law:

- (a + b) = - a - b

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

= 4 lo g_{2} (11) - 6 - 6 lo g_{2} (3)

4 lo g_{2} (11) = lo g_{2} (1 1^{4})

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

= lo g_{2} (1 1^{4}) - 6 - lo g_{2} (3^{6})

lo g_{2} (1 1^{4}) - lo g_{2} (3^{6}) = lo g_{2} (\frac{14641}{729})

= lo g_{2} (\frac{14641}{729}) - 6

ln (\frac{( 3 ^{x} 6 ^{2 x} )}{2 ^{3 x}})

ln (13 x) - ln (13)

5 ln (x) + ln (y)

lo g_{9} (4) + 3 lo g_{9} (x - 1)

lo g_{5} (x yz)

What is 4log_{2}(11)-6log_{2}(6) ?
The solution to 4log_{2}(11)-6log_{2}(6) is log_{2}(14641/729)-6