What is log_{2}((x^3y)/(5z^6)) ?

The solution to log_{2}((x^3y)/(5z^6)) is 3log_{2}(x)+log_{2}(y)-log_{2}(5)-6log_{2}(z)

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simplify log_{2}((x^3y)/(5z^6))

simplify

lo g_{2} (\frac{x ^{3} y}{5 z ^{6}})

3 lo g_{2} (x) + lo g_{2} (y) - lo g_{2} (5) - 6 lo g_{2} (z)

Solution steps

lo g_{2} (\frac{x ^{3} y}{5 z ^{6}})

Apply log rule:

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

lo g_{2} (\frac{x ^{3} y}{5 z ^{6}}) = lo g_{2} (x^{3} y) - lo g_{2} (5 z^{6})

= lo g_{2} (x^{3} y) - lo g_{2} (5 z^{6})

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

lo g_{2} (5 z^{6}) = lo g_{2} (5) + 6 lo g_{2} (z)

= 3 lo g_{2} (x) + lo g_{2} (y) - (lo g_{2} (5) + 6 lo g_{2} (z))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{2} (5) + 6 lo g_{2} (z)) = - lo g_{2} (5) - 6 lo g_{2} (z)

= 3 lo g_{2} (x) + lo g_{2} (y) - lo g_{2} (5) - 6 lo g_{2} (z)

- 4 lo g_{b} (d) + lo g_{b} (e) - 2 lo g_{b} (f)

lo g_{10} (\frac{3 x}{y})

ln ∣ b ∣ - ln ∣ a ∣

lo g_{2} (64 p)

What is log_{2}((x^3y)/(5z^6)) ?
The solution to log_{2}((x^3y)/(5z^6)) is 3log_{2}(x)+log_{2}(y)-log_{2}(5)-6log_{2}(z)