What is expand log_{10}(sqrt(x^7y^{-4)}) ?

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

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expand log_{10}(sqrt(x^7y^{-4)})

expand

lo g_{10} (x^{7} y^{- 4})

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

Solution steps

lo g_{10} (x^{7} y^{- 4})

x^{7} y^{- 4} = \frac{x ^{3} x}{y ^{2}}

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

= lo g_{10} (x^{3} x) - lo g_{10} (y^{2})

Simplify

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

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

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

(b - x + ((x + b) \cdot (5 \cdot b - 3 \cdot x)))^{2}

(x - 2) (x + 6) (x - \frac{1}{2})

(cos (t) \cdot t + 2 sin (t)) \cdot (cos (t))

u (\frac{v - u}{a})

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

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