What is 4log_{2}(3x) ?

The solution to 4log_{2}(3x) is 4log_{2}(3)+4log_{2}(x)

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simplify 4log_{2}(3x)

simplify

4 lo g_{2} (3 x)

4 lo g_{2} (3) + 4 lo g_{2} (x)

Solution steps

4 lo g_{2} (3 x)

Apply log rule:

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

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

= 4 (lo g_{2} (3) + lo g_{2} (x))

Apply the distributive law:

a (b + c) = ab + a c

4 (lo g_{2} (3) + lo g_{2} (x)) = 4 lo g_{2} (3) + 4 lo g_{2} (x)

= 4 lo g_{2} (3) + 4 lo g_{2} (x)

lo g_{10} (24) - lo g_{10} (2)

lo g_{10} (\frac{2.51 \cdot 1 0 ^{- 9}}{x})

- lo g_{10} (4.34 \cdot 1 0^{- 6})

2 lo g_{10} (y^{3}) + lo g_{10} (y^{2})

lo g_{a} (x^{2}) - 2 lo g_{a} (x)