What is expand log_{2}(x/(3y^2)) ?

The solution to expand log_{2}(x/(3y^2)) is log_{2}(x)-log_{2}(3)-2log_{2}(y)

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expand log_{2}(x/(3y^2))

expand

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

lo g_{2} (x) - lo g_{2} (3) - 2 lo g_{2} (y)

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= lo g_{2} (x) - lo g_{2} (3 y^{2})

Apply log rule:

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

lo g_{2} (3 y^{2}) = lo g_{2} (3) + lo g_{2} (y^{2})

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= lo g_{2} (x) - (lo g_{2} (3) + 2 lo g_{2} (y))

- (lo g_{2} (3) + 2 lo g_{2} (y)) : - lo g_{2} (3) - 2 lo g_{2} (y)

= lo g_{2} (x) - lo g_{2} (3) - 2 lo g_{2} (y)

ln ∣ x ∣ - ln x^{2}

- 1423.586575 \cdot lo g_{10} (\frac{0.1}{1})

ln ((x^{2} + \frac{1}{n})^{n}) - ln (x^{2 n})

lo g_{10} (\frac{\frac{1}{256}}{\frac{125}{4}})

ln (1 - x) - ln (1 + x)

What is expand log_{2}(x/(3y^2)) ?
The solution to expand log_{2}(x/(3y^2)) is log_{2}(x)-log_{2}(3)-2log_{2}(y)