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

The solution to log_{2}((x^2y)/z) is 2log_{2}(x)+log_{2}(y)-log_{2}(z)

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simplify log_{2}((x^2y)/z)

simplify

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

2 lo g_{2} (x) + lo g_{2} (y) - lo g_{2} (z)

Solution steps

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

Simplify

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

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

lo g_{10} (7) + 2 lo g_{10} (3) - lo g_{10} (4)

6 ln (x) - \frac{1}{5} ln (y)

3^{\frac{l n ( \frac{4}{l n ( 3 )} )}{l n ( 3 )}} ln (3)

lo g_{8} (7 x)

2 lo g_{10} (a) + 4 lo g_{10} (b^{2}) - lo g_{10} (a) b

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