What is expand log_{10}(sqrt(x^3y^{-6)}) ?

The solution to expand log_{10}(sqrt(x^3y^{-6)}) is 3/2 log_{10}(x)-3log_{10}(y)

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expand log_{10}(sqrt(x^3y^{-6)})

expand

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

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

Solution steps

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

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

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

Apply log rule:

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

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

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

Simplify

lo g_{10} (y^{3}) : 3 lo g_{10} (y)

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

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

\frac{28 e ^{- 20 s + a}}{( s - 7 ) ^{2}}

\frac{1}{( s + 1 ) ( s ^{2} + 1 )}

(1 + t e^{- t})^{3}

(x - 4) (x - 6) (x - 7) (x + 7)

(x - 2 y - 1) d x + (3 x - 6 y + 2) d y

What is expand log_{10}(sqrt(x^3y^{-6)}) ?
The solution to expand log_{10}(sqrt(x^3y^{-6)}) is 3/2 log_{10}(x)-3log_{10}(y)