What is log_{2}(3)+4log_{2}(x)+1/2 log_{2}(y) ?

The solution to log_{2}(3)+4log_{2}(x)+1/2 log_{2}(y) is log_{2}(3x^4y^{1/2})

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simplify log_{2}(3)+4log_{2}(x)+1/2 log_{2}(y)

simplify

lo g_{2} (3) + 4 lo g_{2} (x) + \frac{1}{2} lo g_{2} (y)

lo g_{2} (3 x^{4} y^{\frac{1}{2}})

Solution steps

lo g_{2} (3) + 4 lo g_{2} (x) + \frac{1}{2} lo g_{2} (y)

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) + lo g_{2} (x^{4}) + \frac{1}{2} lo g_{2} (y)

Apply log rule:

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

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

= lo g_{2} (3 x^{4}) + \frac{1}{2} lo g_{2} (y)

Apply log rule:

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

\frac{1}{2} lo g_{2} (y) = lo g_{2} (y^{\frac{1}{2}})

= lo g_{2} (3 x^{4}) + lo g_{2} (y^{\frac{1}{2}})

Apply log rule:

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

lo g_{2} (3 x^{4}) + lo g_{2} (y^{\frac{1}{2}}) = lo g_{2} (3 x^{4} y^{\frac{1}{2}})

= lo g_{2} (3 x^{4} y^{\frac{1}{2}})

- lo g_{10} (0.56) - (1 - 1) \cdot lo g_{10} (1 - 0.56)

lo g_{10} (\frac{x ^{4}}{y ^{5} z})

\frac{1}{12} ln ∣ (12 \cdot 5) + 150 ∣ - \frac{1}{12} ln ∣ 12 + 6 ∣

\frac{3 ln ( 2 ) - ln ( 3 )}{4}

2 lo g_{a} (y - 4) - 5 lo g_{a} (y + 7)

What is log_{2}(3)+4log_{2}(x)+1/2 log_{2}(y) ?
The solution to log_{2}(3)+4log_{2}(x)+1/2 log_{2}(y) is log_{2}(3x^4y^{1/2})