What is log_{2}(4xy^5) ?

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

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simplify log_{2}(4xy^5)

simplify

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

2 + lo g_{2} (x) + 5 lo g_{2} (y)

Solution steps

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

Factor the number:

4 = 2^{2}

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

Apply log rule:

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

lo g_{2} (2^{2} x y^{5}) = lo g_{2} (2^{2}) + lo g_{2} (x y^{5})

= lo g_{2} (2^{2}) + lo g_{2} (x y^{5})

Apply log rule:

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

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

= 2 + lo g_{2} (x y^{5})

Simplify

lo g_{2} (x y^{5}) : lo g_{2} (x) + 5 lo g_{2} (y)

= 2 + (lo g_{2} (x) + 5 lo g_{2} (y))

Apply rule:

a + (b + c) = a + b + c

2 + (lo g_{2} (x) + 5 lo g_{2} (y)) = 2 + lo g_{2} (x) + 5 lo g_{2} (y)

= 2 + lo g_{2} (x) + 5 lo g_{2} (y)

lo g_{b} (343 k)

ln (\frac{sin ( x )}{x})

\frac{1}{2} [6 ln (x - 3) + ln (x) - 2 ln (x)]

lo g_{10} (6) + lo g_{10} (3)

\frac{1}{2} ln (\frac{1}{2})

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