What is log_{2}(3sqrt(y))+4log_{2}(x) ?

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

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simplify log_{2}(3sqrt(y))+4log_{2}(x)

simplify

lo g_{2} (3 y) + 4 lo g_{2} (x)

lo g_{2} (3 y x^{4})

Solution steps

lo g_{2} (3 y) + 4 lo g_{2} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 lo g_{2} (x) = lo g_{2} (x^{4})

= lo g_{2} (3 y) + lo g_{2} (x^{4})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{2} (3 y) + lo g_{2} (x^{4}) = lo g_{2} (3 x^{4} y)

= lo g_{2} (3 y x^{4})

- lo g_{10} (4.8 \cdot 1 0^{- 10})

ln ((9 - x^{2} - y^{2}) (x^{2} + y^{2} - 1))

- lo g_{10} (3 \cdot 1 0^{- 2})

\frac{1}{2} ln (\frac{6 + 3 7}{2})

2717 - lo g_{10} (2 π)

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