What is 3log_{10}(6)-4log_{10}(2)-log_{10}(3) ?

The solution to 3log_{10}(6)-4log_{10}(2)-log_{10}(3) is log_{10}(9/2)

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simplify 3log_{10}(6)-4log_{10}(2)-log_{10}(3)

simplify

3 lo g_{10} (6) - 4 lo g_{10} (2) - lo g_{10} (3)

lo g_{10} (\frac{9}{2})

Decimal Notation

0.65321 \dots

Solution steps

3 lo g_{10} (6) - 4 lo g_{10} (2) - lo g_{10} (3)

3 lo g_{10} (6) = lo g_{10} (6^{3})

- 4 lo g_{10} (2) = - lo g_{10} (2^{4})

= lo g_{10} (6^{3}) - lo g_{10} (2^{4}) - lo g_{10} (3)

Apply log rule:

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

lo g_{10} (6^{3}) - lo g_{10} (2^{4}) = lo g_{10} (\frac{6 ^{3}}{2 ^{4}})

= lo g_{10} (\frac{6 ^{3}}{2 ^{4}}) - lo g_{10} (3)

Apply log rule:

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

lo g_{10} (\frac{6 ^{3}}{2 ^{4}}) - lo g_{10} (3) = lo g_{10} (\frac{\frac{6 ^{3}}{2 ^{4}}}{3})

= lo g_{10} (\frac{\frac{6 ^{3}}{2 ^{4}}}{3})

\frac{\frac{6 ^{3}}{2 ^{4}}}{3} = \frac{9}{2}

= lo g_{10} (\frac{9}{2})

lo g_{2} (\frac{x y ^{2}}{64})

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (7)

12 lo g_{7} (x) - 3 lo g_{7} (y)

6 + 3 ln (\frac{1}{2})

lo g_{2} (\frac{c d ^{3}}{e ^{4}})

What is 3log_{10}(6)-4log_{10}(2)-log_{10}(3) ?
The solution to 3log_{10}(6)-4log_{10}(2)-log_{10}(3) is log_{10}(9/2)