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

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

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simplify 2log_{3}(2x)

simplify

2 lo g_{3} (2 x)

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

Solution steps

2 lo g_{3} (2 x)

Apply log rule:

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

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

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

\frac{1}{5} lo g_{6} (8) - (lo g_{6} (5) + lo g_{6} (3))

lo g_{10} (5) - 2 lo g_{10} (3)

0.6 lo g_{2} (0.6) + 0.4 lo g_{2} (0.4)

lo g_{10} (25) + lo g_{10} (4) + lo g_{10} (2)

lo g_{10} (3) - 2 lo g_{10} (2)