What is log_{2}((2x)^3(x+1)) ?

The solution to log_{2}((2x)^3(x+1)) is 3+3log_{2}(x)+log_{2}(x+1)

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simplify log_{2}((2x)^3(x+1))

simplify

lo g_{2} ((2 x)^{3} (x + 1))

3 + 3 lo g_{2} (x) + lo g_{2} (x + 1)

Solution steps

lo g_{2} ((2 x)^{3} (x + 1))

Simplify

(2 x)^{3} (x + 1) : 8 x^{3} (x + 1)

= lo g_{2} (8 x^{3} (x + 1))

Factor the number:

8 = 2^{3}

= lo g_{2} (2^{3} x^{3} (x + 1))

Apply log rule:

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

lo g_{2} (2^{3} x^{3} (x + 1)) = lo g_{2} (2^{3}) + lo g_{2} (x^{3} (x + 1))

= lo g_{2} (2^{3}) + lo g_{2} (x^{3} (x + 1))

Apply log rule:

lo g_{a} (a^{b}) = b

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

= 3 + lo g_{2} (x^{3} (x + 1))

Simplify

lo g_{2} (x^{3} (x + 1)) : 3 lo g_{2} (x) + lo g_{2} (x + 1)

= 3 + (3 lo g_{2} (x) + lo g_{2} (x + 1))

Apply rule:

a + (b + c) = a + b + c

3 + (3 lo g_{2} (x) + lo g_{2} (x + 1)) = 3 + 3 lo g_{2} (x) + lo g_{2} (x + 1)

= 3 + 3 lo g_{2} (x) + lo g_{2} (x + 1)

8 lo g_{10} (x) + lo g_{10} (y) - lo g_{10} (z)

ln (x x^{2} + 1)

lo g_{7} (49 k)

- lo g_{10} (1.8 x 1 0^{- 5})

2 lo g_{10} (3) + lo g_{10} (4)

What is log_{2}((2x)^3(x+1)) ?
The solution to log_{2}((2x)^3(x+1)) is 3+3log_{2}(x)+log_{2}(x+1)