What is expand log_{10}(sqrt(x^7y^{-10)}) ?

The solution to expand log_{10}(sqrt(x^7y^{-10)}) is 7/2 log_{10}(x)-5log_{10}(y)

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expand log_{10}(sqrt(x^7y^{-10)})

expand

lo g_{10} (x^{7} y^{- 10})

\frac{7}{2} lo g_{10} (x) - 5 lo g_{10} (y)

Solution steps

lo g_{10} (x^{7} y^{- 10})

x^{7} y^{- 10} = \frac{x ^{3} x}{y ^{5}}

= lo g_{10} (\frac{x ^{3} 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 ^{3} x}{y ^{5}}) = lo g_{10} (x^{3} x) - lo g_{10} (y^{5})

= lo g_{10} (x^{3} x) - lo g_{10} (y^{5})

Simplify

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

lo g_{10} (x^{3} x) = \frac{7}{2} lo g_{10} (x)

= \frac{7}{2} lo g_{10} (x) - 5 lo g_{10} (y)

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

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

\frac{d}{d x} ((z) (2 x^{2} y + 3 x z + 5 y z^{2} - 10))

(sin (x) + 1) (- sin (x))

(x + (\frac{1}{x})) \cdot (1 + \frac{2}{x ^{2} - 1})

What is expand log_{10}(sqrt(x^7y^{-10)}) ?
The solution to expand log_{10}(sqrt(x^7y^{-10)}) is 7/2 log_{10}(x)-5log_{10}(y)