What is log_{2}(x^4sqrt(y^5)) ?

The solution to log_{2}(x^4sqrt(y^5)) is 4log_{2}(x)+2log_{2}(y)+log_{2}(sqrt(y))

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simplify log_{2}(x^4sqrt(y^5))

simplify

lo g_{2} (x^{4} y^{5})

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

Solution steps

lo g_{2} (x^{4} y^{5})

Simplify

y^{5} : y^{2} y

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

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

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

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

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

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

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

lo g_{5} (u) + 6 lo g_{5} (v)

1 + lo g_{10} (x) + lo g_{10} (2)

lo g_{2} (\frac{y}{4})

lo g_{10} (\frac{11 c}{4})

lo g_{10} (x^{2} - 9) - lo g_{10} (x + 3)

What is log_{2}(x^4sqrt(y^5)) ?
The solution to log_{2}(x^4sqrt(y^5)) is 4log_{2}(x)+2log_{2}(y)+log_{2}(sqrt(y))