What is log_{2}((9x)/y) ?

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

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simplify log_{2}((9x)/y)

simplify

lo g_{2} (\frac{9 x}{y})

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

Solution steps

lo g_{2} (\frac{9 x}{y})

Apply log rule:

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

lo g_{2} (\frac{9 x}{y}) = lo g_{2} (9 x) - lo g_{2} (y)

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

Simplify

lo g_{2} (9 x) : 2 lo g_{2} (3) + lo g_{2} (x)

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

lo g_{b} (\frac{16}{25})

5 lo g_{10} (x) + lo g_{10} (20) - lo g_{10} (10)

lo g_{10} (80) - 2 \cdot lo g_{10} (4)

lo g_{5} (\frac{x}{25 y ^{3}})

lo g_{10} (a) + 3 lo g_{10} (c)

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