What is 3log_{2}(3)-12log_{2}(7) ?

The solution to 3log_{2}(3)-12log_{2}(7) is log_{2}((27)/(7^{12)})

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simplify 3log_{2}(3)-12log_{2}(7)

simplify

3 lo g_{2} (3) - 12 lo g_{2} (7)

lo g_{2} (\frac{27}{7 ^{12}})

Decimal Notation

- 28.93337 \dots

Solution steps

3 lo g_{2} (3) - 12 lo g_{2} (7)

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

- 12 lo g_{2} (7) = - lo g_{2} (7^{12})

= lo g_{2} (3^{3}) - lo g_{2} (7^{12})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{2} (3^{3}) - lo g_{2} (7^{12}) = lo g_{2} (\frac{3 ^{3}}{7 ^{12}})

= lo g_{2} (\frac{3 ^{3}}{7 ^{12}})

3^{3} = 27

= lo g_{2} (\frac{27}{7 ^{12}})

lo g_{7} (x) - lo g_{7} (x^{3})

lo g_{2} (\frac{4}{x + 7})

\frac{1}{lo g _{2} ( 10 ) - lo g _{2} ( 9 )}

lo g_{10} (5 x + 1) - lo g_{10} (x)

lo g_{8} (\frac{f}{64})

What is 3log_{2}(3)-12log_{2}(7) ?
The solution to 3log_{2}(3)-12log_{2}(7) is log_{2}((27)/(7^{12)})