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Popular >

simplify log_{x}(1/4)

Solution

simplify

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

Solution

- 2 lo g_{x} (2)

Solution steps

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

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

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

Apply log rule:

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

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

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

Apply rule:

1 \cdot a = a

= - lo g_{x} (4)

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

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

= - 2 lo g_{x} (2)

Popular Examples

simplify 192ln(s/(762))-s+763 simplify

192 ln (\frac{s}{762}) - s + 763

simplify log_{10}(75x^2)simplify

lo g_{10} (75 x^{2})

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lo g_{3} (x) + lo g_{3} (6 x) - lo g_{3} (x^{2})

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lo g_{10} (x + 5) + lo g_{10} (x + 1)

simplify 6log_{9}(z)+1/2*log_{9}(x)simplify

6 lo g_{9} (z) + \frac{1}{2} \cdot lo g_{9} (x)

Frequently Asked Questions (FAQ)

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