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Popular >

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

Solution

expand

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

Solution

\frac{3}{2} lo g_{10} (x) - 2 lo g_{10} (y)

Solution steps

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

x^{3} y^{- 4} = \frac{x x}{y ^{2}}

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

Apply log rule:

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

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

= lo g_{10} (x x) - lo g_{10} (y^{2})

Simplify

lo g_{10} (y^{2}) : 2 lo g_{10} (y)

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

= \frac{3}{2} lo g_{10} (x) - 2 lo g_{10} (y)

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Frequently Asked Questions (FAQ)

What is expand log_{10}(sqrt(x^3y^{-4)}) ?
The solution to expand log_{10}(sqrt(x^3y^{-4)}) is 3/2 log_{10}(x)-2log_{10}(y)