What is expand log_{10}(3x^4y^{-7}) ?

The solution to expand log_{10}(3x^4y^{-7}) is log_{10}(3)+4log_{10}(x)-7log_{10}(y)

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expand log_{10}(3x^4y^{-7})

expand

lo g_{10} (3 x^{4} y^{- 7})

lo g_{10} (3) + 4 lo g_{10} (x) - 7 lo g_{10} (y)

Solution steps

lo g_{10} (3 x^{4} y^{- 7})

Apply log rule:

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

lo g_{10} (3 x^{4} y^{- 7}) = lo g_{10} (3) + lo g_{10} (x^{4}) + lo g_{10} (y^{- 7})

= lo g_{10} (3) + lo g_{10} (x^{4}) + lo g_{10} (y^{- 7})

Apply log rule:

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

lo g_{10} (x^{4}) = 4 lo g_{10} (x)

= lo g_{10} (3) + 4 lo g_{10} (x) + lo g_{10} (y^{- 7})

Apply log rule:

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

lo g_{10} (y^{- 7}) = - 7 lo g_{10} (y)

= lo g_{10} (3) + 4 lo g_{10} (x) - 7 lo g_{10} (y)

ln (x y z^{2})

ln (2 + 1) - ln (2 - 1)

lo g_{10} (\frac{y ^{2} \cdot x}{3 z})

lo g_{7} (x) - lo g_{7} (x^{9})

ln (\frac{6}{e ^{4}})

What is expand log_{10}(3x^4y^{-7}) ?
The solution to expand log_{10}(3x^4y^{-7}) is log_{10}(3)+4log_{10}(x)-7log_{10}(y)