What is 3log_{2}(6)-log_{2}(6.75) ?

The solution to 3log_{2}(6)-log_{2}(6.75) is 5

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simplify 3log_{2}(6)-log_{2}(6.75)

simplify

3 lo g_{2} (6) - lo g_{2} (6.75)

5

Solution steps

3 lo g_{2} (6) - lo g_{2} (6.75)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

= lo g_{2} (6^{3}) - lo g_{2} (6.75)

Apply log rule:

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

lo g_{2} (6^{3}) - lo g_{2} (6.75) = lo g_{2} (\frac{6 ^{3}}{6.75})

= lo g_{2} (\frac{6 ^{3}}{6.75})

\frac{6 ^{3}}{6.75} = 32

= lo g_{2} (32)

Factor the number:

32 = 2^{5}

= lo g_{2} (2^{5})

Apply log rule:

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

= 5

ln (\frac{1}{( 2 π x ) ^{N}})

2 lo g_{c} (z) - \frac{1}{5} lo g_{c} (y) + 6 lo g_{c} (x)

- lo g_{10} (4.25 \cdot 1 0^{- 5})

\frac{1}{3} ln (3 r^{2} s)

0.9 ln (3) + 2.4 ln (0.75)

What is 3log_{2}(6)-log_{2}(6.75) ?
The solution to 3log_{2}(6)-log_{2}(6.75) is 5