Question

if a=b^2x,b=c^2y,c=^2z,find the value of xyz

Answer 1

$a = b^{2x}\\ taking\ log\ on\ both\ sides\\ log\ a=log\ (b^{2x})\\ \Rightarrow log\ a=2x\ log\ b\\ \Rightarrow 2x= \frac{log\ b}{log\ a} \\ \Rightarrow x= \frac{log\ b}{2\ log\ a} \\ \\Similarly,\\ y= \frac{log\ c}{2\ log\ b}\\z= \frac{log\ a}{2\ log\ c}\\ \\ xyz=\frac{log\ b}{2\ log\ a} \times \frac{log\ c}{2\ log\ b} \times \frac{log\ a}{2\ log\ c}= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8}$