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Popular >

simplify log_{4}(1/9)

Solution

simplify

lo g_{4} (\frac{1}{9})

Solution

- lo g_{2} (3)

+1

Decimal

- 1.58496 \dots

Solution steps

lo g_{4} (\frac{1}{9})

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

= lo g_{4} (9^{- 1})

Apply log rule:

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

lo g_{4} (9^{- 1}) = - 1 \cdot lo g_{4} (9)

= - 1 \cdot lo g_{4} (9)

Factor the number:

9 = 3^{2}

= - 1 \cdot lo g_{4} (3^{2})

Apply log rule:

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

lo g_{4} (3^{2}) = 2 lo g_{4} (3)

= - 1 \cdot 2 lo g_{4} (3)

Factor the number:

4 = 2^{2}

= - 1 \cdot 2 lo g_{2^{2}} (3)

Apply log rule:

lo g_{a^{b}} (x) = \frac{1}{b} lo g_{a} (x), a > 0

lo g_{2^{2}} (3) = \frac{1}{2} lo g_{2} (3)

= - 1 \cdot 2 \cdot \frac{1}{2} lo g_{2} (3)

2 \cdot \frac{1}{2} lo g_{2} (3) = lo g_{2} (3)

= - 1 \cdot lo g_{2} (3)

Apply rule:

1 \cdot a = a

= - lo g_{2} (3)

Popular Examples

8 y = \frac{16}{7}

- 6 x \leq - 19

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10 x y^{3} \cdot 8 x^{5} y^{3}

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factor 7a^2-62a-9 factor

7 a^{2} - 62 a - 9

Frequently Asked Questions (FAQ)

What is log_{4}(1/9) ?
The solution to log_{4}(1/9) is -log_{2}(3)