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

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

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

simplify

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

- lo g_{10} (3)

Decimal Notation

- 0.47712 \dots

Solution steps

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

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

Cancel the numbers:

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

= lo g_{10} (\frac{1}{3})

\frac{1}{3} = 3^{- 1}

= lo g_{10} (3^{- 1})

Apply log rule:

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

lo g_{10} (3^{- 1}) = - 1 \cdot lo g_{10} (3)

= - 1 \cdot lo g_{10} (3)

Apply rule:

1 \cdot a = a

= - lo g_{10} (3)

ln (1 + 2) - ln (- 1 + 2)

lo g_{10} (\frac{x ^{4} y}{z})

\frac{1}{2} lo g_{a} (x) - 3 lo g_{a} (y) + 6 lo g_{a} (z)

- lo g_{b} (\frac{1}{8})

ln (x) + ln (x - 1)

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