Suppose 4a = 5, 5b = 6, 6c = 7, 7d = 8, then the value of abcd is = ?

Answer: Option B

$$\begin{array}{rl}& 8=7^d\\ & ={\left(6^c\right)}^d\\ & ={\left(5^b\right)}^{cd}\\ & =5^{bcd}\\ & ={\left(4^a\right)}^{bcd}\\ & =4^{abcd}\\ & \Rightarrow 4^{abcd}=8\\ & \Rightarrow {\left(2^2\right)}^{abcd}=2^3\\ & \Rightarrow 2abcd=3\\ & \Rightarrow abcd=\frac{3}{2}\end{array}$$