Question

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

Answer 1

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.

Answer 2

Answer:

1

Step-by-step explanation:

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