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Popular >

simplify log_{3}(0.1)

Solution

simplify

lo g_{3} (0.1)

Solution

- lo g_{3} (10)

+1

Decimal Notation

- 2.09590 \dots

Solution steps

lo g_{3} (0.1)

0.1 = \frac{1}{10}

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

\frac{1}{10} = 1 0^{- 1}

= lo g_{3} (1 0^{- 1})

Apply log rule:

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

lo g_{3} (1 0^{- 1}) = - 1 \cdot lo g_{3} (10)

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

Apply rule:

1 \cdot a = a

= - lo g_{3} (10)

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Frequently Asked Questions (FAQ)

What is log_{3}(0.1) ?
The solution to log_{3}(0.1) is -log_{3}(10)