What is expand log_{10}(sqrt((xy^2)/(z^8))) ?

The solution to expand log_{10}(sqrt((xy^2)/(z^8))) is log_{10}(y)+1/2 log_{10}(x)-4log_{10}(z)

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expand log_{10}(sqrt((xy^2)/(z^8)))

expand

lo g_{10} (\frac{x y ^{2}}{z ^{8}})

lo g_{10} (y) + \frac{1}{2} lo g_{10} (x) - 4 lo g_{10} (z)

Solution steps

lo g_{10} (\frac{x y ^{2}}{z ^{8}})

\frac{x y ^{2}}{z ^{8}} = \frac{y x}{z ^{4}}

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

Apply log rule:

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

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

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

Simplify

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

lo g_{10} (y x) = lo g_{10} (y) + \frac{1}{2} lo g_{10} (x)

= lo g_{10} (y) + \frac{1}{2} lo g_{10} (x) - 4 lo g_{10} (z)

\frac{x + 7}{( x + 3 ) ^{2}}

43 (36 - 21) - 2 (52 + 47)

\frac{( x + h ) ^{3}}{h}

(3 x^{2} y - 4 x y^{3} + 6 x) d x + (x^{3} - 6 x^{2} y^{2} - 1) d y

What is expand log_{10}(sqrt((xy^2)/(z^8))) ?
The solution to expand log_{10}(sqrt((xy^2)/(z^8))) is log_{10}(y)+1/2 log_{10}(x)-4log_{10}(z)