Let α,β,γ are positive integers and logα(3x−5y−z)=logβ(x+8z)= – InterviewSolution

1.	Let α,β,γ are positive integers and logα(3x−5y−z)=logβ(x+8z)=logγ(y−3z−x)(wherever defined). If logαa=2,log2β2b=4,log4γ216c=5(a,b,c>0) then value of (a8)(b4)(c2)is
Answer» Let $α, β, γ$ are positive integers and $\frac{log α}{(3 x - 5 y - z)} = \frac{log β}{(x + 8 z)} = \frac{log γ}{(y - 3 z - x)}$ (wherever defined). If ${log}_{α} a = 2, {log}_{2 β} 2 b = 4, {log}_{4 γ^{2}} 16 c = 5 (a, b, c > 0)$ then value of $(\frac{a}{8}) (\frac{b}{4}) (\frac{c}{2})$ is

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