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Popular >

simplify log_{4}(0.0625)

Solution

simplify

lo g_{4} (0.0625)

Solution

- 2

Solution steps

lo g_{4} (0.0625)

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (0.0625)

Apply log rule:

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

lo g_{2^{2}} (0.0625) = \frac{1}{2} lo g_{2} (0.0625)

= \frac{1}{2} lo g_{2} (0.0625)

0.0625 = \frac{625}{10000}

= \frac{1}{2} lo g_{2} (\frac{625}{10000})

\frac{625}{10000} = 2^{- 4}

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

Apply log rule:

lo g_{a} (a^{b}) = b

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

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

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

= - 2

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Frequently Asked Questions (FAQ)

What is log_{4}(0.0625) ?
The solution to log_{4}(0.0625) is -2