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Popular >

simplify log_{4}(1/128)

Solution

simplify

lo g_{4} (\frac{1}{128})

Solution

- \frac{7}{2}

+1

Solution steps

lo g_{4} (\frac{1}{128})

Factor the number:

4 = 2^{2}

= lo g_{2^{2}} (\frac{1}{128})

Apply log rule:

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

lo g_{2^{2}} (\frac{1}{128}) = \frac{1}{2} lo g_{2} (\frac{1}{128})

= \frac{1}{2} lo g_{2} (\frac{1}{128})

\frac{1}{128} = 2^{- 7}

= \frac{1}{2} lo g_{2} (2^{- 7})

Apply log rule:

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

lo g_{2} (2^{- 7}) = - 7

= \frac{1}{2} (- 7)

\frac{1}{2} (- 7) = - \frac{7}{2}

= - \frac{7}{2}

Popular Examples

factor x^5-3x^4-16x+48 factor

x^{5} - 3 x^{4} - 16 x + 48

\frac{4}{7} \div \frac{1}{3}

factor 20x^2+45 factor

20 x^{2} + 45

simplify 21\times 7 simplify

21 \times 7

simplify 4/80 simplify

\frac{4}{80}

Frequently Asked Questions (FAQ)

What is log_{4}(1/128) ?
The solution to log_{4}(1/128) is -7/2