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Popular >

simplify-log_{b}(1/5)

Solution

simplify

- lo g_{b} (\frac{1}{5})

Solution

lo g_{b} (5)

Solution steps

- lo g_{b} (\frac{1}{5})

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

= - lo g_{b} (5^{- 1})

Apply log rule:

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

lo g_{b} (5^{- 1}) = - 1 \cdot lo g_{b} (5)

= - (- 1 \cdot lo g_{b} (5))

Apply rule:

1 \cdot a = a

- 1 \cdot lo g_{b} (5) = - lo g_{b} (5)

= - (- lo g_{b} (5))

Apply rule:

- (- a) = a

- (- lo g_{b} (5)) = lo g_{b} (5)

= lo g_{b} (5)

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Frequently Asked Questions (FAQ)

What is simplify-log_{b}(1/5) ?
The solution to simplify-log_{b}(1/5) is log_{b}(5)