What is expand log_{10}(sqrt(x^5*y^{-8)}) ?

The solution to expand log_{10}(sqrt(x^5*y^{-8)}) is 5/2 log_{10}(x)-4log_{10}(y)

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expand log_{10}(sqrt(x^5*y^{-8)})

expand

lo g_{10} (x^{5} \cdot y^{- 8})

\frac{5}{2} lo g_{10} (x) - 4 lo g_{10} (y)

Solution steps

lo g_{10} (x^{5} y^{- 8})

x^{5} y^{- 8} = \frac{x ^{2} x}{y ^{4}}

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

= lo g_{10} (x^{2} x) - lo g_{10} (y^{4})

Simplify

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

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

= \frac{5}{2} lo g_{10} (x) - 4 lo g_{10} (y)

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

(3 + 2 i)^{4}

(3 + 2 i)^{3}

(x + 6) (x - 6)

\frac{1}{( 1 - i ) ^{5}}

What is expand log_{10}(sqrt(x^5*y^{-8)}) ?
The solution to expand log_{10}(sqrt(x^5*y^{-8)}) is 5/2 log_{10}(x)-4log_{10}(y)