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

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

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

simplify

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

lo g_{10} (\frac{3}{4})

Decimal Notation

- 0.12493 \dots

Solution steps

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

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

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

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

Apply log rule:

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

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

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

Cancel

\frac{3 ^{3}}{6 ^{2}} : \frac{3}{4}

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

\frac{1}{4} lo g_{10} (2 x + y) - lo g_{10} (3 x + 2 y)

lo g_{9} (10) - lo g_{9} (7)

ln (\frac{e ^{9}}{12})

lo g_{10} (\frac{x ^{2} y ^{5}}{z ^{3}})

lo g_{2} (x) - lo g_{2} (x^{4})

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