Question

$\frac{1}{log_{\sqrt{bc}} abc}+\frac{1}{log_{\sqrt{ca}} abc}+\frac{1}{log_{\sqrt{ab}} abc}$ has the value equal to-

• A. 1/2
• B. 1
• C. 2
• D. 4

Answer 1

Answer: (B)

1

Answer 2

Using the property $\frac{1}{log_x y} = log_y x$, the expression becomes $log_{abc} \sqrt{bc} + log_{abc} \sqrt{ca} + log_{abc} \sqrt{ab}$. Using $log_b x + log_b y + log_b z = log_b (xyz)$, this simplifies to $log_{abc} (\sqrt{bc} \cdot \sqrt{ca} \cdot \sqrt{ab})$. The argument simplifies to $\sqrt{a^2 b^2 c^2} = abc$. Thus, the expression is $log_{abc} abc = 1$.