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Popular >

simplify log_{5}(5x^{-5})

Solution

simplify

lo g_{5} (5 x^{- 5})

Solution

1 - 5 lo g_{5} (x)

Solution steps

lo g_{5} (5 x^{- 5})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{5} (5 x^{- 5}) = lo g_{5} (5) + lo g_{5} (x^{- 5})

= lo g_{5} (5) + lo g_{5} (x^{- 5})

Apply log rule:

lo g_{a} (a) = 1

lo g_{5} (5) = 1

= 1 + lo g_{5} (x^{- 5})

Apply log rule

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

lo g_{5} (x^{- 5}) = - 5 lo g_{5} (x)

= 1 - 5 lo g_{5} (x)

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Frequently Asked Questions (FAQ)

What is log_{5}(5x^{-5}) ?
The solution to log_{5}(5x^{-5}) is 1-5log_{5}(x)