What is log_{2}((xy^2)/(64)) ?

The solution to log_{2}((xy^2)/(64)) is log_{2}(x)+2log_{2}(y)-6

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simplify log_{2}((xy^2)/(64))

simplify

lo g_{2} (\frac{x y ^{2}}{64})

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

Solution steps

lo g_{2} (\frac{x y ^{2}}{64})

Apply log rule:

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

lo g_{2} (\frac{x y ^{2}}{64}) = lo g_{2} (x y^{2}) - lo g_{2} (64)

= lo g_{2} (x y^{2}) - lo g_{2} (64)

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

lo g_{2} (64) = 6

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

\frac{1}{2} lo g_{2} (3) - 2 lo g_{2} (7)

12 lo g_{7} (x) - 3 lo g_{7} (y)

6 + 3 ln (\frac{1}{2})

lo g_{2} (\frac{c d ^{3}}{e ^{4}})

lo g_{10} (8^{2}) - lo g_{10} (12 5^{2})

What is log_{2}((xy^2)/(64)) ?
The solution to log_{2}((xy^2)/(64)) is log_{2}(x)+2log_{2}(y)-6