Question

If x = 1 +${\log }_a$ bc, y = 1 + ${\log }_b$ ca, z = 1 + ${\log }_c$ ab. Find the value of xy + yz + zx.

• A. + +
• B. xyz
• C. + +
• D. 1

Answer 1

The correct option is B xyz

Given x = 1 + ${\log }_a$ $bc=lo{g}_{a}a+lo{g}_{a}bc=lo{g}_{a}abc$
$\Rightarrow \frac{1}{x}=lo{g}_{abc}a$
Similarly $\frac{1}{y}={\log }_{abc}b,\frac{1}{z}=lo{g}_{abc}c$
$\therefore \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=lo{g}_{abc}a+lo{g}_{abc}b+lo{g}_{abc}c$
$=lo{g}_{abc}abc=1$
$\Rightarrow \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\Rightarrow xy+yz+zx=xyz$