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Popular >

simplify log_{a}(1/27)

Solution

simplify

lo g_{a} (\frac{1}{27})

Solution

- 3 lo g_{a} (3)

Solution steps

lo g_{a} (\frac{1}{27})

\frac{1}{27} = 2 7^{- 1}

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

Apply log rule:

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

lo g_{a} (2 7^{- 1}) = - 1 \cdot lo g_{a} (27)

= - 1 \cdot lo g_{a} (27)

Apply rule:

1 \cdot a = a

= - lo g_{a} (27)

Factor the number:

27 = 3^{3}

= - lo g_{a} (3^{3})

Apply log rule:

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

- lo g_{a} (3^{3}) = - 3 lo g_{a} (3)

= - 3 lo g_{a} (3)

Popular Examples

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expand log_{12}((12)/y)expand

lo g_{12} (\frac{12}{y})

Frequently Asked Questions (FAQ)

What is log_{a}(1/27) ?
The solution to log_{a}(1/27) is -3log_{a}(3)