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Popular >

simplify log_{1/4}(2)

Solution

simplify

lo g_{\frac{1}{4}} (2)

Solution

- \frac{1}{2}

+1

Decimal Notation

- 0.5

Solution steps

lo g_{\frac{1}{4}} (2)

Apply log rule:

lo g_{\frac{1}{a}} (x) = - lo g_{a} (x)

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

= - lo g_{4} (2)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= - \frac{1}{2} \cdot 1

Multiply the numbers:

\frac{1}{2} \cdot 1 = \frac{1}{2}

= - \frac{1}{2}

Popular Examples

factor y^2+6y+5 factor

y^{2} + 6 y + 5

16 x^{2} - 3 = 78

2 x^{2} = 36

3 (y - 6)^{2} = 72

y^{2} = 2 y + 63

Frequently Asked Questions (FAQ)

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