What is log_{2}(7)+3log_{2}(x)-log_{2}(y) ?

The solution to log_{2}(7)+3log_{2}(x)-log_{2}(y) is log_{2}((7x^3)/y)

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simplify log_{2}(7)+3log_{2}(x)-log_{2}(y)

simplify

lo g_{2} (7) + 3 lo g_{2} (x) - lo g_{2} (y)

lo g_{2} (\frac{7 x ^{3}}{y})

Solution steps

lo g_{2} (7) + 3 lo g_{2} (x) - lo g_{2} (y)

Apply log rule:

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

lo g_{2} (7) - lo g_{2} (y) = lo g_{2} (\frac{7}{y})

= lo g_{2} (\frac{7}{y}) + 3 lo g_{2} (x)

Apply log rule:

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

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

= lo g_{2} (\frac{7}{y}) + lo g_{2} (x^{3})

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{2} (\frac{7}{y}) + lo g_{2} (x^{3}) = lo g_{2} (\frac{7}{y} x^{3})

= lo g_{2} (\frac{7}{y} x^{3})

Simplify

\frac{7}{y} x^{3} : \frac{7 x ^{3}}{y}

= lo g_{2} (\frac{7 x ^{3}}{y})

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

lo g_{10} (1000 x^{3} y^{5})

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

ln (\frac{9}{2})

\frac{1}{3} (lo g_{10} (x) - 2 lo g_{10} (y))

What is log_{2}(7)+3log_{2}(x)-log_{2}(y) ?
The solution to log_{2}(7)+3log_{2}(x)-log_{2}(y) is log_{2}((7x^3)/y)