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

The solution to log_{2}(2xy^2) is 1+log_{2}(x)+2log_{2}(y)

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simplify log_{2}(2xy^2)

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 1 + lo g_{2} (x y^{2})

Simplify

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

= 1 + (lo g_{2} (x) + 2 lo g_{2} (y))

Apply rule:

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

1 + (lo g_{2} (x) + 2 lo g_{2} (y)) = 1 + lo g_{2} (x) + 2 lo g_{2} (y)

= 1 + lo g_{2} (x) + 2 lo g_{2} (y)

ln (\frac{e}{13})

lo g_{10} (\frac{x}{1000 y ^{6}})

lo g_{2} (\frac{x ^{3} y ^{8}}{5})

\frac{ln ( x )}{2} - 4 ln (y) - \frac{1}{3} ln (x + 2)

- \frac{1}{2} + \frac{1}{4} lo g_{10} (0.1) + \frac{1}{2} lo g_{10} (a)

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