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Popular >

simplify log_{x}(1/81)

Solution

simplify

lo g_{x} (\frac{1}{81})

Solution

- 4 lo g_{x} (3)

Solution steps

lo g_{x} (\frac{1}{81})

\frac{1}{81} = 8 1^{- 1}

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

Apply log rule:

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

lo g_{x} (8 1^{- 1}) = - 1 \cdot lo g_{x} (81)

= - 1 \cdot lo g_{x} (81)

Apply rule:

1 \cdot a = a

= - lo g_{x} (81)

Factor the number:

81 = 3^{4}

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

Apply log rule:

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

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

= - 4 lo g_{x} (3)

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Frequently Asked Questions (FAQ)

What is log_{x}(1/81) ?
The solution to log_{x}(1/81) is -4log_{x}(3)