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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

2 lo g_{10} (a) + 2 lo g_{10} (b)

lo g_{4} (17 x)

lo g_{3} (\frac{z}{27})

ln (3) + \frac{1}{3} ln (64)

lo g_{a} (\frac{x ^{2} y}{z ^{3}})

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