What is log_{10}(8)-2log_{10}(6)-log_{10}(3) ?

The solution to log_{10}(8)-2log_{10}(6)-log_{10}(3) is log_{10}(2/27)

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simplify log_{10}(8)-2log_{10}(6)-log_{10}(3)

simplify

lo g_{10} (8) - 2 lo g_{10} (6) - lo g_{10} (3)

lo g_{10} (\frac{2}{27})

Decimal Notation

- 1.13033 \dots

Solution steps

lo g_{10} (8) - 2 lo g_{10} (6) - lo g_{10} (3)

lo g_{10} (8) = 3 lo g_{10} (2)

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

3 lo g_{10} (2) = lo g_{10} (2^{3})

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

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

Apply log rule:

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

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

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

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

\frac{\frac{2 ^{3}}{6 ^{2}}}{3} = \frac{2}{27}

= lo g_{10} (\frac{2}{27})

ln (\frac{4}{4 + 2})

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

lo g_{5} (4 x^{7})

lo g_{2} (\frac{3}{2 x})

lo g_{a} (\frac{x ^{4}}{y ^{2} a ^{7}})

What is log_{10}(8)-2log_{10}(6)-log_{10}(3) ?
The solution to log_{10}(8)-2log_{10}(6)-log_{10}(3) is log_{10}(2/27)