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

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

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

simplify

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

- lo g_{10} (2)

Decimal Notation

- 0.30102 \dots

Solution steps

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

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

Cancel the numbers:

\frac{3}{6} = \frac{1}{2}

= lo g_{10} (\frac{1}{2})

\frac{1}{2} = 2^{- 1}

= lo g_{10} (2^{- 1})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (2^{- 1}) = - 1 \cdot lo g_{10} (2)

= - 1 \cdot lo g_{10} (2)

Apply rule:

1 \cdot a = a

= - lo g_{10} (2)

lo g_{10} (x (x + 2))

(\frac{1}{2})^{3} - 24 ln (\frac{1}{2}) + 5

lo g_{10} (20) - lo g_{10} (4)

lo g_{10} (200 \cdot 0. 1^{x}) + lo g_{10} (500 \cdot 100 0^{y})

- lo g_{10} (2 \cdot 1 0^{- 9})

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