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Popular >

simplify log_{3}(1/16)

Solution

simplify

lo g_{3} (\frac{1}{16})

Solution

- 4 lo g_{3} (2)

+1

Decimal Notation

- 2.52371 \dots

Solution steps

lo g_{3} (\frac{1}{16})

\frac{1}{16} = 1 6^{- 1}

= lo g_{3} (1 6^{- 1})

Apply log rule:

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

lo g_{3} (1 6^{- 1}) = - 1 \cdot lo g_{3} (16)

= - 1 \cdot lo g_{3} (16)

Apply rule:

1 \cdot a = a

= - lo g_{3} (16)

Factor the number:

16 = 2^{4}

= - lo g_{3} (2^{4})

Apply log rule:

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

- lo g_{3} (2^{4}) = - 4 lo g_{3} (2)

= - 4 lo g_{3} (2)

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Frequently Asked Questions (FAQ)

What is log_{3}(1/16) ?
The solution to log_{3}(1/16) is -4log_{3}(2)