What is log_{10}(sqrt(x^3y^{-4)}) ?

The solution to log_{10}(sqrt(x^3y^{-4)}) is log_{10}(x)+log_{10}(sqrt(x))-2log_{10}(y)

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simplify log_{10}(sqrt(x^3y^{-4)})

simplify

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

lo g_{10} (x) + lo g_{10} (x) - 2 lo g_{10} (y)

Solution steps

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

Simplify

x^{3} y^{- 4} : \frac{x x}{y ^{2}}

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

lo g_{10} (x x) = lo g_{10} (x) + lo g_{10} (x)

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

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

(x^{m} + x^{n})^{2}

2 (3 - 2 i) - 2 (5 - 4 i)

lo g_{8} (x) - lo g_{\frac{1}{4}} (y) + lo g_{2} (z)

\frac{( 36 x ^{3} y ^{7} z ^{4} )}{( 12 x ^{2} y ^{2} )}

24 \times 24

What is log_{10}(sqrt(x^3y^{-4)}) ?
The solution to log_{10}(sqrt(x^3y^{-4)}) is log_{10}(x)+log_{10}(sqrt(x))-2log_{10}(y)