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

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

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

simplify

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

lo g_{10} (2)

Decimal Notation

0.30102 \dots

Solution steps

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

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

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

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

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

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{10} (3^{2}) + lo g_{10} (2^{3}) = lo g_{10} (3^{2} \cdot 2^{3})

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

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

Cancel

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

= lo g_{10} (2)

2 (lo g_{a} (x) - lo g_{a} (y + 1) + lo g_{a} (z))

\frac{1}{2} (lo g_{2} (a) + lo g_{2} (b))

lo g_{10} (x^{5}) y

ln (x) - ln (\frac{1}{x})

0.7 \cdot lo g_{10} (1 \cdot 1 0^{- 3}) + 0.1

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