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Popular >

simplify log_{3}(1/4)

Solution

simplify

lo g_{3} (\frac{1}{4})

Solution

- 2 lo g_{3} (2)

+1

Decimal Notation

- 1.26185 \dots

Solution steps

lo g_{3} (\frac{1}{4})

\frac{1}{4} = 4^{- 1}

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

Apply log rule:

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

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

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

Apply rule:

1 \cdot a = a

= - lo g_{3} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= - 2 lo g_{3} (2)

Popular Examples

x^{2} + 2 x + 1 = 2 x + 5

factor 8m^2n^2-24mn^3+16mn factor

8 m^{2} n^{2} - 24 m n^{3} + 16 mn

- 5 x - 2 \leq 3

x^{2} + 9 x + 4 = - x + 4

factor 4x^3(4x-8)^2+x^4(2)(4x-8)(8)factor

4 x^{3} (4 x - 8)^{2} + x^{4} (2) (4 x - 8) (8)

Frequently Asked Questions (FAQ)

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