What is log_{2}(5)+log_{2}(x)-log_{2}(3) ?

The solution to log_{2}(5)+log_{2}(x)-log_{2}(3) is log_{2}((5x)/3)

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simplify log_{2}(5)+log_{2}(x)-log_{2}(3)

simplify

lo g_{2} (5) + lo g_{2} (x) - lo g_{2} (3)

lo g_{2} (\frac{5 x}{3})

Solution steps

lo g_{2} (5) + lo g_{2} (x) - lo g_{2} (3)

Apply log rule:

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

lo g_{2} (5) + lo g_{2} (x) = lo g_{2} (5 x)

= lo g_{2} (5 x) - lo g_{2} (3)

Apply log rule:

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

lo g_{2} (5 x) - lo g_{2} (3) = lo g_{2} (\frac{5 x}{3})

= lo g_{2} (\frac{5 x}{3})

lo g_{10} (5 t)

8 lo g_{b} (x) + 9 lo g_{b} (z)

lo g_{4} (5) - lo g_{4} (9)

lo g_{2} (x + 1) - lo g_{2} (x - 1)

\frac{1}{9} (lo g_{2} (z) + 4 lo g_{2} (y))

What is log_{2}(5)+log_{2}(x)-log_{2}(3) ?
The solution to log_{2}(5)+log_{2}(x)-log_{2}(3) is log_{2}((5x)/3)