1/(1 + loga bc) + (1 + logb ca) + (1 + logc ab)(1) 0(2) 1(3) abc(4) 1/

1.	1/(1 + loga bc) + (1 + logb ca) + (1 + logc ab)(1) 0(2) 1(3) abc(4) 1/abc
Answer» ANSWER: Option 2 is CORRECT. Step-by-step explanation: To find VALUE of expression: $\frac{1}{1+log_a\:bc}+\frac{1}{1+log_b\:ca}+\frac{1}{1+log_c\:ab}$ We use the following result, $log_c\:x=\frac{log\:x}{log\:c}\:and\:log\,xy=\log\,x+log\,y$ Consider, $\frac{1}{1+log_a\:bc}+\frac{1}{1+log_b\:ca}+\frac{1}{1+log_c\:ab}$ $\implies\frac{1}{1+\frac{log\,bc}{log\,a}}+\frac{1}{1+\frac{log\,ca}{log\,b}}+\frac{1}{1+\frac{log\,ab}{log\,c}}$ $\implies\frac{log\,a}{log\,a+log\,bc}+\frac{log\,b}{log\,b+log\,ca}+\frac{log\,c}{log\,c+log\,ab}$ $\implies\frac{log\,a}{log\,a+log\,b+log\,c}+\frac{log\,b}{log\,b+log\,c+log\,a}+\frac{log\,c}{log\,c+log\,a+log\,b}$ $\implies\frac{log\,a+log\,b+log\,c}{log\,b+log\,c+log\,a}$ $\implies1$ Therefore, Option 2 is correct.