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Popular >

simplify log_{2}(1/9)

Solution

simplify

lo g_{2} (\frac{1}{9})

Solution

- 2 lo g_{2} (3)

+1

Decimal Notation

- 3.16992 \dots

Solution steps

lo g_{2} (\frac{1}{9})

\frac{1}{9} = 9^{- 1}

= lo g_{2} (9^{- 1})

Apply log rule:

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

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

= - 1 \cdot lo g_{2} (9)

Apply rule:

1 \cdot a = a

= - lo g_{2} (9)

Factor the number:

9 = 3^{2}

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

Apply log rule:

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

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

= - 2 lo g_{2} (3)

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Frequently Asked Questions (FAQ)

What is log_{2}(1/9) ?
The solution to log_{2}(1/9) is -2log_{2}(3)