What is expand log_{10}(sqrt(x^7y^{-12)}) ?

The solution to expand log_{10}(sqrt(x^7y^{-12)}) is 7/2 log_{10}(x)-6log_{10}(y)

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expand log_{10}(sqrt(x^7y^{-12)})

expand

lo g_{10} (x^{7} y^{- 12})

\frac{7}{2} lo g_{10} (x) - 6 lo g_{10} (y)

Solution steps

lo g_{10} (x^{7} y^{- 12})

x^{7} y^{- 12} = \frac{x ^{3} x}{y ^{6}}

= lo g_{10} (\frac{x ^{3} x}{y ^{6}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{x ^{3} x}{y ^{6}}) = lo g_{10} (x^{3} x) - lo g_{10} (y^{6})

= lo g_{10} (x^{3} x) - lo g_{10} (y^{6})

Simplify

lo g_{10} (y^{6}) : 6 lo g_{10} (y)

lo g_{10} (x^{3} x) = \frac{7}{2} lo g_{10} (x)

= \frac{7}{2} lo g_{10} (x) - 6 lo g_{10} (y)

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What is expand log_{10}(sqrt(x^7y^{-12)}) ?
The solution to expand log_{10}(sqrt(x^7y^{-12)}) is 7/2 log_{10}(x)-6log_{10}(y)