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Popular >

simplify log_{10}(1/3)

Solution

simplify

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

Solution

- lo g_{10} (3)

+1

Decimal Notation

- 0.47712 \dots

Solution steps

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)

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Frequently Asked Questions (FAQ)

What is log_{10}(1/3) ?
The solution to log_{10}(1/3) is -log_{10}(3)