What is expand log_{10}(sqrt(x^5y^{-10)}) ?

The solution to expand log_{10}(sqrt(x^5y^{-10)}) is 5/2 log_{10}(x)-5log_{10}(y)

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expand log_{10}(sqrt(x^5y^{-10)})

expand

lo g_{10} (x^{5} y^{- 10})

\frac{5}{2} lo g_{10} (x) - 5 lo g_{10} (y)

Solution steps

lo g_{10} (x^{5} y^{- 10})

x^{5} y^{- 10} = \frac{x ^{2} x}{y ^{5}}

= lo g_{10} (\frac{x ^{2} x}{y ^{5}})

Apply log rule:

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

lo g_{10} (\frac{x ^{2} x}{y ^{5}}) = lo g_{10} (x^{2} x) - lo g_{10} (y^{5})

= lo g_{10} (x^{2} x) - lo g_{10} (y^{5})

Simplify

lo g_{10} (y^{5}) : 5 lo g_{10} (y)

lo g_{10} (x^{2} x) = \frac{5}{2} lo g_{10} (x)

= \frac{5}{2} lo g_{10} (x) - 5 lo g_{10} (y)

\frac{( 1 + 2 e ^{t} ) ^{3}}{27}

\frac{I n ( 2 - 3 x )}{x ^{2} - 36}

(3 (n + 1))!

(x + 2)^{2}

- \frac{4 x}{( x ^{2} - 1 ) ^{2}}

What is expand log_{10}(sqrt(x^5y^{-10)}) ?
The solution to expand log_{10}(sqrt(x^5y^{-10)}) is 5/2 log_{10}(x)-5log_{10}(y)