What is log_{2}((x^3+2)sqrt((x-5)^3)) ?

The solution to log_{2}((x^3+2)sqrt((x-5)^3)) is log_{2}(x^3+2)+log_{2}(sqrt((x-5)^2)sqrt(x-5))

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simplify log_{2}((x^3+2)sqrt((x-5)^3))

simplify

lo g_{2} ((x^{3} + 2) (x - 5)^{3})

lo g_{2} (x^{3} + 2) + lo g_{2} ((x - 5)^{2} x - 5)

Solution steps

lo g_{2} ((x^{3} + 2) (x - 5)^{3})

Apply log rule:

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

lo g_{2} ((x^{3} + 2) (x - 5)^{3}) = lo g_{2} (x^{3} + 2) + lo g_{2} ((x - 5)^{3})

= lo g_{2} (x^{3} + 2) + lo g_{2} ((x - 5)^{3})

(x - 5)^{3} = (x - 5)^{2} x - 5

= lo g_{2} (x^{3} + 2) + lo g_{2} ((x - 5)^{2} x - 5)

\frac{1}{0.0105} ln (\frac{6000}{5000})

ln (\frac{25}{50})

ln (n) - ln (n - 1)

lo g_{10} (\frac{6}{z})

(ln ∣ 1 - 3 ∣ - ln ∣ 0 - 3 ∣) - (ln ∣ 1 + 3 ∣ - ln ∣ 0 + 3 ∣)

What is log_{2}((x^3+2)sqrt((x-5)^3)) ?
The solution to log_{2}((x^3+2)sqrt((x-5)^3)) is log_{2}(x^3+2)+log_{2}(sqrt((x-5)^2)sqrt(x-5))