A) \[1/2\]
B) \[1\]
C) \[2\]
D) \[1/3\]
Correct Answer: C
Solution :
[c] \[{{a}^{x}}=bc,\] \[{{b}^{y}}=ca,\] \[{{c}^{z}}=ab\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,x={{\log }_{a}}bc,\,\,y={{\log }_{b}}ac,\,\,z={{\log }_{c}}ab\] \[\Rightarrow \,\,\,\,\,\,\,\,\frac{x}{1+x}+\frac{y}{1+y}+\frac{z}{1+z}=\frac{{{\log }_{a}}bc}{{{\log }_{a}}abc}+\frac{{{\log }_{b}}ac}{{{\log }_{b}}abc}\] \[+\frac{{{\log }_{c}}ab}{{{\log }_{c}}abc}\] \[={{\log }_{abc}}bc+{{\log }_{abc}}ac+{{\log }_{abc}}ab\] \[={{\log }_{abc}}{{(abc)}^{2}}=2\]
You need to login to perform this action.
You will be redirected in
3 sec
