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Popular >

simplify log_{64}(1/16)

Solution

simplify

lo g_{64} (\frac{1}{16})

Solution

- \frac{2}{3}

+1

Decimal Notation

- 0.66666 \dots

Solution steps

lo g_{64} (\frac{1}{16})

Factor the number:

64 = 2^{6}

= lo g_{2^{6}} (\frac{1}{16})

Apply log rule:

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

lo g_{2^{6}} (\frac{1}{16}) = \frac{1}{6} lo g_{2} (\frac{1}{16})

= \frac{1}{6} lo g_{2} (\frac{1}{16})

\frac{1}{16} = 2^{- 4}

= \frac{1}{6} lo g_{2} (2^{- 4})

Apply log rule:

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

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

= \frac{1}{6} (- 4)

\frac{1}{6} (- 4) = - \frac{2}{3}

= - \frac{2}{3}

Popular Examples

simplify (-15/7)-(-7/5)simplify

(- \frac{15}{7}) - (- \frac{7}{5})

simplify 16-16/3 simplify

16 - \frac{16}{3}

r^{2} - 8 r + 9 = 0

simplify 8*5 simplify

8 \cdot 5

1-2/3 \times 2/3

1 - \frac{2}{3} \times \frac{2}{3}

Frequently Asked Questions (FAQ)

What is log_{64}(1/16) ?
The solution to log_{64}(1/16) is -2/3