What is log_{2}((x^3+2)sqrt((x-4)^3)) ?

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

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simplify log_{2}((x^3+2)sqrt((x-4)^3))

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

(x - 4)^{3} = (x - 4)^{2} x - 4

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

- lo g_{10} (3.2 \cdot 1 0^{- 8})

- lo g_{10} (1.1 \cdot 1 0^{- 6})

- 2 (ln (100 - x) - 2 ln (10))

4 lo g_{10} (x - 9) - 5 lo g_{10} (x)

6 lo g_{10} (x) + 7 lo g_{10} (y)

What is log_{2}((x^3+2)sqrt((x-4)^3)) ?
The solution to log_{2}((x^3+2)sqrt((x-4)^3)) is log_{2}(x^3+2)+log_{2}(sqrt((x-4)^2)sqrt(x-4))