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Popular >

simplify log_{10}(1/64)

Solution

simplify

lo g_{10} (\frac{1}{64})

Solution

- 6 lo g_{10} (2)

+1

Decimal Notation

- 1.80617 \dots

Solution steps

lo g_{10} (\frac{1}{64})

\frac{1}{64} = 6 4^{- 1}

= lo g_{10} (6 4^{- 1})

Apply log rule:

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

lo g_{10} (6 4^{- 1}) = - 1 \cdot lo g_{10} (64)

= - 1 \cdot lo g_{10} (64)

Apply rule:

1 \cdot a = a

= - lo g_{10} (64)

Factor the number:

64 = 2^{6}

= - lo g_{10} (2^{6})

Apply log rule:

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

- lo g_{10} (2^{6}) = - 6 lo g_{10} (2)

= - 6 lo g_{10} (2)

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Frequently Asked Questions (FAQ)

What is log_{10}(1/64) ?
The solution to log_{10}(1/64) is -6log_{10}(2)