What is log_{2}(9xy) ?

The solution to log_{2}(9xy) is 2log_{2}(3)+log_{2}(x)+log_{2}(y)

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simplify log_{2}(9xy)

simplify

lo g_{2} (9 x y)

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

Solution steps

lo g_{2} (9 x y)

Apply log rule:

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

lo g_{2} (9 x y) = lo g_{2} (9) + lo g_{2} (x) + lo g_{2} (y)

= lo g_{2} (9) + lo g_{2} (x) + lo g_{2} (y)

lo g_{2} (9) = 2 lo g_{2} (3)

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

3 ln (y - x)

- \frac{3}{8} \cdot lo g_{2} (\frac{3}{8}) - \frac{5}{8} \cdot lo g_{2} (\frac{5}{8})

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

\frac{1}{2} lo g_{6} (x) + lo g_{6} (y)

lo g_{5} (8) + lo g_{5} (3)

What is log_{2}(9xy) ?
The solution to log_{2}(9xy) is 2log_{2}(3)+log_{2}(x)+log_{2}(y)