Question

solve the above question. ​

Answer 1

Solution:

$\mathrm{\therefore\dfrac{1}{log_{a}(abc)}+\dfrac{1}{log_{b}(abc)}+\dfrac{1}{log_{c}(abc)}}$

$\mathrm{=\dfrac{1}{\dfrac{log(abc)}{log(a)}}+\dfrac{1}{\dfrac{log(abc)}{log(b)}}+\dfrac{1}{\dfrac{log(abc)}{log(c)}}}$

$\mathrm{=\dfrac{log(a)}{log(abc)}+\dfrac{log(b)}{log(abc)}+\dfrac{log(c)}{log(abc)}}$

$\mathrm{=\dfrac{log(a)+log(b)+log(c)}{log(abc)}}$

$\mathrm{=\dfrac{log(abc)}{log(abc)}}$

$\mathrm{=1}$

Answer: Option (2) $\mathrm{1}$ is correct.