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Popular >

simplify log_{b}(1/8)

Solution

simplify

lo g_{b} (\frac{1}{8})

Solution

- 3 lo g_{b} (2)

Solution steps

lo g_{b} (\frac{1}{8})

\frac{1}{8} = 8^{- 1}

= lo g_{b} (8^{- 1})

Apply log rule:

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

lo g_{b} (8^{- 1}) = - 1 \cdot lo g_{b} (8)

= - 1 \cdot lo g_{b} (8)

Apply rule:

1 \cdot a = a

= - lo g_{b} (8)

Factor the number:

8 = 2^{3}

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

Apply log rule:

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

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

= - 3 lo g_{b} (2)

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Frequently Asked Questions (FAQ)

What is log_{b}(1/8) ?
The solution to log_{b}(1/8) is -3log_{b}(2)