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Popular >

simplify log_{a}(1/25)

Solution

simplify

lo g_{a} (\frac{1}{25})

Solution

- 2 lo g_{a} (5)

Solution steps

lo g_{a} (\frac{1}{25})

\frac{1}{25} = 2 5^{- 1}

= lo g_{a} (2 5^{- 1})

Apply log rule:

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

lo g_{a} (2 5^{- 1}) = - 1 \cdot lo g_{a} (25)

= - 1 \cdot lo g_{a} (25)

Apply rule:

1 \cdot a = a

= - lo g_{a} (25)

Factor the number:

25 = 5^{2}

= - lo g_{a} (5^{2})

Apply log rule:

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

- lo g_{a} (5^{2}) = - 2 lo g_{a} (5)

= - 2 lo g_{a} (5)

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Frequently Asked Questions (FAQ)

What is log_{a}(1/25) ?
The solution to log_{a}(1/25) is -2log_{a}(5)