1logab×1logbc×1logcaisequalto - 1logab×1logbc×1logcaisequalto - \eqalign{ & \frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}} \cr & {\text{is}}\,{\text{equal}}\,{\text{to - }} \cr} " /> 1logab×1logbc×1logcaisequalto - 1logab×1logbc×1logcaisequalto - \eqalign{ & \frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}} \cr & {\text{is}}\,{\text{equal}}\,{\text{to - }} \cr} " /> 1logab×1logbc×1logcaisequalto - 1logab×1logbc×1logcaisequalto - \eqalign{ & \frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}} \cr & {\text{is}}\,{\text{equal}}\,{\text{to - }} \cr} " />

India’s No.1 Educational Platform For UPSC,PSC And All Competitive Exam

Download Our App

$\begin{aligned} \frac{1}{\log_{a} b} \times \frac{1}{\log_{b} c} \times \frac{1}{\log_{c} a} \\ is equal to - \end{aligned}$ $\eqalign{ & \frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}} \cr & {\text{is}}\,{\text{equal}}\,{\text{to - }} \cr}$

1a+b+c
2abc
30
41

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given Expression \\ (\frac{\log a}{\log b} \times \frac{\log b}{\log c} \times \frac{\log c}{\log a}) \\ = 1 \end{aligned}

$\eqalign{ & {\text{Given}}\,\,\,{\text{Expression}} \cr & \left( {\frac{{\log a}}{{\log b}} \times \frac{{\log b}}{{\log c}} \times \frac{{\log c}}{{\log a}}} \right) \cr & = 1 \cr}$

Workspace Report

Post your Comments

", "text": "

\begin{aligned} \frac{1}{\log_{a} b} \times \frac{1}{\log_{b} c} \times \frac{1}{\log_{c} a} \\ is equal to - \end{aligned}

$\eqalign{ & \frac{1}{{{{\log }_a}b}} \times \frac{1}{{{{\log }_b}c}} \times \frac{1}{{{{\log }_c}a}} \cr & {\text{is}}\,{\text{equal}}\,{\text{to - }} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Given Expression \\ (\frac{\log a}{\log b} \times \frac{\log b}{\log c} \times \frac{\log c}{\log a}) \\ = 1 \end{aligned}

$\eqalign{ & {\text{Given}}\,\,\,{\text{Expression}} \cr & \left( {\frac{{\log a}}{{\log b}} \times \frac{{\log b}}{{\log c}} \times \frac{{\log c}}{{\log a}}} \right) \cr & = 1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution: