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

The solution to 3log_{10}(6)-2log_{10}(3) is log_{10}(24)

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

simplify

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

lo g_{10} (24)

Decimal Notation

1.38021 \dots

Solution steps

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

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

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

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

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

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

Cancel

\frac{6 ^{3}}{3 ^{2}} : 24

= lo g_{10} (24)

lo g_{3} (4) - lo g_{3} (5)

2 lo g_{a} (y) - lo g_{a} (z)

2 ln (x + 4) - 8 ln (x)

- lo g_{10} (6.3 \cdot 1 0^{- 6})

ln (\frac{x ^{2}}{2})

What is 3log_{10}(6)-2log_{10}(3) ?
The solution to 3log_{10}(6)-2log_{10}(3) is log_{10}(24)