Discussion Forum



1)

$\frac{1}{\log_{xy}{xyz}}+\frac{1}{\log_{yz}{xyz}}+\frac{1}{\log_{zx}{xyz}}$ is


A) 1

B) 2

C) log 2

D) $\frac{1}{2}$

Answer:

Option B

Explanation:

$\frac{1}{\log_{xy}{xyz}}+\frac{1}{\log_{yz}{xyz}}+\frac{1}{\log_{zx}{xyz}}$ 

= $\log_{xyz}{xy}+\log_{xyz}{yz}+\log_{xyz}{zx}$

=$ \log_{xyz}{xy\times yz\times zx}$

=$\log_{xyz}{(xyz)^{2}}$

=$2\log_{xyz}{xyz}$

=2\times 1

=2