What is expand log_{5}(5x^{-5}) ?

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

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

expand

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

1 - 5 lo g_{5} (x)

Solution steps

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

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

Apply log rule:

lo g_{a} (a) = 1

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

lo g_{7} (y) - 3 lo g_{7} (z) + \frac{1}{3} lo g_{7} (x)

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\frac{32 ln ( \frac{3}{1201} )}{ln ( 2 )}

e^{\frac{l n ( 3 ) - l n ( 8 ) + l n ( \frac{25}{6} )}{2}}

ln (\frac{e ^{- \frac{1}{2 x}}}{1 - e ^{- \frac{1}{x}}})

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