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help pls!

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Let a, b, and c be the roots of $$24x^3 - 121x^2 + 87x - 8 = 0.$$Find $$\log_3(a)+\log_3(b)+\log_3(c)$$

im stuck on this problem, and my parents forgot how to do logs😂...

any help would be appreciated! thank you so much!

Mar 27, 2022

#1
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sum of roots is 121/24

$$a+b+c=\frac{121}{24}\\ ab+ac+bc=\frac{87}{24}=\frac{29}{8}\\ abc=\frac{8}{24}=\frac{1}{3}$$

$$\log_3(a)+\log_3(b)+\log_3(c)\\ =log_3(abc)\\ =log_3(\frac{1}{3})\\ =log_3(3^{-1})\\ =-1log_3(3)\\ =-1$$

Mar 27, 2022