What is expand log_{10}(sqrt(x^3y^{-8)}) ?

The solution to expand log_{10}(sqrt(x^3y^{-8)}) is 3/2 log_{10}(x)-4log_{10}(y)

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expand log_{10}(sqrt(x^3y^{-8)})

expand

lo g_{10} (x^{3} y^{- 8})

\frac{3}{2} lo g_{10} (x) - 4 lo g_{10} (y)

Solution steps

lo g_{10} (x^{3} y^{- 8})

x^{3} y^{- 8} = \frac{x x}{y ^{4}}

= lo g_{10} (\frac{x x}{y ^{4}})

Apply log rule:

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

lo g_{10} (\frac{x x}{y ^{4}}) = lo g_{10} (x x) - lo g_{10} (y^{4})

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

Simplify

lo g_{10} (y^{4}) : 4 lo g_{10} (y)

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

= \frac{3}{2} lo g_{10} (x) - 4 lo g_{10} (y)

\frac{n ( 1 + n )}{2}

sin (7 x^{2} (x - 3))

\frac{( 2 + 2 x ) ^{4}}{( 1 + x 3 ) ^{6}}

\frac{x y ( y + 2 ) ( y - 2 )}{y + 6}

6 a \cdot (5 - 3)

What is expand log_{10}(sqrt(x^3y^{-8)}) ?
The solution to expand log_{10}(sqrt(x^3y^{-8)}) is 3/2 log_{10}(x)-4log_{10}(y)