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

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

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

simplify

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

lo g_{10} (\frac{3}{2})

Decimal Notation

0.17609 \dots

Solution steps

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

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

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

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

Apply log rule:

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

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

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

Cancel

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

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

900 (ln (301.13) - ln (278))

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ln (x y z^{3})

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