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Question Number 167215 by Avijit007 last updated on 09/Mar/22

Answered by MikeH last updated on 09/Mar/22

$${\log }_{b}a\times {\log }_{c}b\times {\log }_{a}c=$$$$\frac{1}{\cancel{{\log }_{a}b}}\times \frac{\cancel{{\log }_{a}b}}{{\log }_{a}c}\times {\log }_{a}c=1$$

Answered by MikeH last updated on 09/Mar/22

$$\mathrm{Now},$$$${\log }_{\sqrt{\mathrm{a}}}\mathrm{b}\times {\log }_{\sqrt{\mathrm{b}}}\mathrm{c}\times {\log }_{\sqrt{\mathrm{c}}}\mathrm{a}=$$$${2\log }_{\mathrm{a}}\mathrm{b}\times {2\log }_{\mathrm{b}}\mathrm{c}\times {2\log }_{\mathrm{c}}\mathrm{a}=$$$$8\left({\log }_{\mathrm{a}}\mathrm{b}\times {\log }_{\mathrm{b}}\mathrm{c}\times {\log }_{\mathrm{c}}\mathrm{a}\right)=$$$$8\left(1\right)=8$$

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