What is expand log_{10}(sqrt(x^7y^{-8)}) ?

The solution to expand log_{10}(sqrt(x^7y^{-8)}) is 7/2 log_{10}(x)-4log_{10}(y)

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expand log_{10}(sqrt(x^7y^{-8)})

expand

lo g_{10} (x^{7} y^{- 8})

\frac{7}{2} lo g_{10} (x) - 4 lo g_{10} (y)

Solution steps

lo g_{10} (x^{7} y^{- 8})

x^{7} y^{- 8} = \frac{x ^{3} x}{y ^{4}}

= lo g_{10} (\frac{x ^{3} 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 ^{3} x}{y ^{4}}) = lo g_{10} (x^{3} x) - lo g_{10} (y^{4})

= lo g_{10} (x^{3} x) - lo g_{10} (y^{4})

Simplify

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

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

= \frac{7}{2} lo g_{10} (x) - 4 lo g_{10} (y)

\frac{s}{( s ^{2} + 16 ) ^{2}}

(x - 4) (x + 2)

(1 + 2 e^{t})^{3}

(9 e - 8 f) (9 e + 8 f)

1 + 2 (x - \frac{π}{4})

What is expand log_{10}(sqrt(x^7y^{-8)}) ?
The solution to expand log_{10}(sqrt(x^7y^{-8)}) is 7/2 log_{10}(x)-4log_{10}(y)