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

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

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simplify log_{2}((3x)^3)

simplify

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

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

Solution steps

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

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

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

= 3 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)

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

(x + z)^{3}

(x + 2)^{11}

sin (x) x^{- 1}

(- 3)^{6} x (- 3)^{5}

- 1 n + 5 n

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