What is expand log_{10}(sqrt(x^5y^{-4)}) ?

The solution to expand log_{10}(sqrt(x^5y^{-4)}) is 5/2 log_{10}(x)-2log_{10}(y)

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expand log_{10}(sqrt(x^5y^{-4)})

expand

lo g_{10} (x^{5} y^{- 4})

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

Solution steps

lo g_{10} (x^{5} y^{- 4})

x^{5} y^{- 4} = \frac{x ^{2} x}{y ^{2}}

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

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

Simplify

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

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

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

(1 - cos^{2} (x))^{2}

\frac{x ( 2 x ^{2} - 5 )}{2 y ( y ^{2} - 2 )}

- \frac{2 ( 3 5 - 5 )}{5} + 1

\frac{1}{( x + 7 ) ^{2}}

\frac{e ^{- 5 s} ( 2 s + 3 )}{( s ^{2} + 2 s + 5 ) ( s )}

What is expand log_{10}(sqrt(x^5y^{-4)}) ?
The solution to expand log_{10}(sqrt(x^5y^{-4)}) is 5/2 log_{10}(x)-2log_{10}(y)