What is log_{2}((8x)/(sqrt(y))) ?

The solution to log_{2}((8x)/(sqrt(y))) is 3+log_{2}(x)-log_{2}(sqrt(y))

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simplify log_{2}((8x)/(sqrt(y)))

simplify

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

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

Solution steps

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

Apply log rule:

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

lo g_{2} (\frac{8 x}{y}) = lo g_{2} (8 x) - lo g_{2} (y)

= lo g_{2} (8 x) - lo g_{2} (y)

Simplify

lo g_{2} (8 x) : 3 + lo g_{2} (x)

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

5 lo g_{10} (x) - 4 lo g_{10} (x^{2} + 1) + 3 lo g_{10} (x - 1)

lo g_{4} (x - 3) + lo g_{4} (x + 3)

lo g_{10} (\frac{x}{1000})

lo g_{10} (\frac{x ^{3}}{y ^{4}})

What is log_{2}((8x)/(sqrt(y))) ?
The solution to log_{2}((8x)/(sqrt(y))) is 3+log_{2}(x)-log_{2}(sqrt(y))